System and method for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing

Abstract

Exemplary embodiments of the present disclosure are directed towards a system and method for hardware-driven low-dimensional numerical representation for enhanced data compression, compact memory address representation, and efficient data indexing. The system introduces base-100 numeral structure known as Gole Number System, wherein each of 100 uniquely designed symbols maps to decimal value from 0 to 99. The system further supports compact memory address representation using extended base-128 symbol set called Evishta. Processor receives numerical input in decimal format, converts it into a base-100 representation using a Binary to Gole Converter (BCG), and maps each digit to corresponding Gole symbol. The encoded Gole symbols are stored in memory array optimized for space efficiency and retrieved for display rendering. A display unit renders the Gole symbols using reduced pixel dimensions per character, thereby minimizing pixel usage and reducing power consumption. The system is scalable across data storage, digital computation, memory representation, and user interface applications.

Description

“SYSTEM AND METHOD FOR HARDWARE-DRIVEN LOWDIMENSIONAL NUMERICAL REPRESENTATION FOR ENHANCED DATA COMPRESSION AND INDEXING”TECHNICAL FIELD

[0001] The present disclosure generally relates to the field of numerical representation and hardware optimization systems. More particularly, the present disclosure relates to a system and method for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing.BACKGROUND

[0002] Numbers are fundamental to nearly every aspect of human life, from simple counting to complex mathematical operations and precise measurements. The decimal number system has been the cornerstone of numerical representation, serving as the standard for various applications, including scientific calculations and data indexing. However, the widespread use of the decimal system comes with inherent limitations, particularly when representing large numbers within a constrained dimensional space.

[0003] For instance, consider the distance between the Earth and the Moon, which is approximately 384,400 kilometers. In the conventional decimal system, representing such a distance requires six digits, occupying a significant amount of space. As our reliance on data continues to grow exponentially in the digital age, the need for efficient storage and processing of vast datasets becomes increasingly critical.

[0004] In many applications, including database indexing and data processing, integers represented in decimal form serve as essential indices. Despite the underlying binary storage in computer memory, human-readable representations often utilize decimal numbers for indexing purposes. However, as datasets expand in size and complexity, the length of these decimal representations growsaccordingly, leading to increased memory requirements and higher hardware demands. Furthermore, the reliance on conventional numerical representations poses challenges in terms of power efficiency and hardware optimization.To optimize computation and address these challenges, Hexadecimal number system has been introduced to make compact memory address representation to some extent however innovative approaches are needed to revolutionize numerical representation. By integrating hardware-driven techniques with low-dimensional numerical representations, it becomes possible to enhance data compression and indexing capabilities. This innovative approach has the potential to significantly reduce memory usage, lower hardware requirements, and improve power efficiency, thereby transforming how we handle and process vast amounts of data across various domains.

[0005] In light of these challenges, there is a pressing need for innovative solutions that can revolutionize numerical representation and address the limitations of the current systems. By introducing a novel approach that combines hardware -driven techniques with low-dimensional numerical representations, it becomes possible to achieve enhanced data compression and indexing capabilities. This innovation has the potential to significantly reduce memory usage, lower hardware requirements, and improve power efficiency, thereby revolutionizing the way we handle and process vast amounts of data in various domains.SUMMARY

[0006] The following presents a simplified summary of the disclosure in order to provide a basic understanding of the reader. This summary is not an extensive overview of the disclosure and it does not identify key / critical elements of the invention or delineate the scope of the invention. Its sole purpose is to present some concepts disclosed herein in a simplified form as a prelude to the more detailed description that is presented later.

[0007] Exemplary embodiments of the present disclosure are directed towards asystem and method for hardware -driven low-dimensional numerical representation for enhanced data compression, indexing, and compact memory address representation.

[0008] An objective of the present disclosure is directed towards a system that introduces a novel numerical representation system called RNumber, enabling the precise representation of large numbers using only half of the digits compared to conventional decimal representation.

[0009] Another objective of the present disclosure is directed towards a system that minimizes hardware requirements for storing high-volume data with power efficiency through the introduction of the enhanced RNumber system.

[0010] Another obj ective of the present disclosure is directed towards a system that proposes an extended number representation, requiring fewer symbols to represent indices or memory addresses compared to conventional systems.

[0011] Another objective of the present disclosure is directed towards a system that implements the RNumber system on smaller hardware platforms compared to conventional systems, thereby achieving power efficiency and hardware optimization.

[0012] Another objective of the present disclosure is directed towards a system that efficiently compresses data and indexes it using the RNumber system, reducing memory usage and enhancing data processing efficiency.

[0013] Another objective ofthe present disclosure is directed towards a system that simplifies numerical operations by utilizing the RNumber system, reducing computational overhead, and improving system responsiveness.

[0014] Another objective of the present disclosure is directed towards a system thatoptimizes resource allocation within computing environments by leveraging the efficient hardware utilization of the RNumber system.

[0015] Another objective ofthe present disclosure is directed towards a system that enhances data security and integrity through the compact and tamper-resistant nature of RNumber representations.

[0016] Another obj ective of the present disclosure is directed towards a system that adapts seamlessly to emerging technologies and computing paradigms, ensuring its continued relevance and effectiveness.

[0017] Another obj ective of the present disclosure is directed towards a system that streamlines data processing pipelines by adopting the RNumber system, reducing latency and enabling real-time decision-making.

[0018] Another objective of the present disclosure is directed towards a system that simplifies data representation, making numerical data easier to interpret and manipulate for users.

[0019] Another obj ective of the present disclosure is directed towards a system that scales performance seamlessly with growing data demands, ensuring consistent performance across diverse workload scenarios.

[0020] Another objective of the present disclosure is directed towards a system that empowers organizations to gain a competitive edge through improved data management and processing capabilities provided by the RNumber system.

[0021] Another objective of the present disclosure is directed towards a system that sets a new standard for efficiency and performance in data-intensive applications through the innovative approach of the RNumber system.

[0022] Another objective of the present disclosure is directed towards a system that enhances the usability and accessibility of numerical data, enabling users to extract actionable insights more efficiently.

[0023] Another objective of the present disclosure is directed towards a system that enables organizations to innovate rapidly, respond to market changes effectively, and capitalize on new opportunities for growth and expansion through the adoption of the RNumber system.

[0024] Another objective of the present disclosure is directed towards a system that improves operational excellence and achieves strategic objectives by leveraging the advanced technologies embodied in the RNumber system.

[0025] Another objective of the present disclosure is directed towards a system that empowers users with industry-leading efficiency and performance in data-intensive applications, setting new benchmarks for excellence.

[0026] Another objective of the present disclosure is directed towards a system that fosters collaboration and innovation by providing a platform for continuous improvement and advancement in numerical representation and data processing technologies.

[0027] Another objective of the present disclosure is directed towards a system that transforms the way organizations handle and process data, unlocking new possibilities for productivity, efficiency, and growth in a rapidly evolving digital landscape.

[0028] Another objective of the present disclosure is directed towards a system that incorporates an adaptive base system within the RNumber framework, enabling flexibility in numerical representation to accommodate varying precision requirements and optimize resource utilization.

[0029] Another objective of the present disclosure is directed towards a system that extends the applicability of the RNumber system beyond traditional numerical domains, finding utility in diverse fields such as finance, telecommunications, and scientific computing, where it addresses unique data storage and processing challenges.

[0030] Another objective of the present disclosure is directed towards a system that embodies a patentable innovation in the form of the RNumber system, offering a novel approach to numerical representation that delivers tangible benefits in terms of efficiency, scalability, and versatility.

[0031] Another objective of the present disclosure is directed towards a system that provides companies and organizations with a competitive advantage through the adoption of the RNumber system, enabling them to optimize their data infrastructure, reduce costs, and enhance performance in a data-driven world.

[0032] Another objective of the present disclosure is directed towards a system that revolutionizes the representation of numbers in mathematics, offering a novel approach to numerical representation that enhances precision and efficiency in mathematical operations.

[0033] Another objective of the present disclosure is directed towards a system that transforms the representation of numbers in programming devices, providing a streamlined and efficient method for handling numerical data in software applications and algorithms.

[0034] Another objective of the present disclosure is directed towards a system that enables the representation of large numbers in a compressed format across various media platforms, addressing scalability concerns and optimizing resource utilization. For example, the RNumber system can alleviate potential shortages ofmobile numbers by efficiently representing them in compressed formats, ensuring universal access without the need for expanding number lengths.

[0035] Another objective of the present disclosure is directed towards a system that introduces a new representation method for providing unique identification numbers to the entire global population using fewer digits. This innovative approach facilitates efficient and scalable identification systems, enhancing accessibility and management of demographic data.

[0036] Another objective of the present disclosure is directed towards a system that explores the representation of numbers in the context of quantum information theory, leveraging the principles of quantum computing to achieve enhanced data representation and processing capabilities.

[0037] Another objective of the present disclosure is directed towards a system that conserves memory resources by representing large numbers and sequences in lowdimensional space, optimizing storage efficiency without sacrificing precision or accuracy.

[0038] Another objective of the present disclosure is directed towards a system that introduces an improved hardware design tailored for memory and power efficiency, enhancing the performance and sustainability of computing devices and systems.

[0039] Another objective of the present disclosure is directed towards a system that introduces the Gole Number System, an evolved base- 100 representation derived from the RNumber concept, incorporating 100 uniquely designed symbols for optimized numerical encoding.

[0040] Another objective of the present disclosure is directed towards a system that implements a compact visual representation format for numbers, dates, and times using the Gole Number System, thereby minimizing the display area required forrendering information on digital screens.

[0041] Another objective of the present disclosure is directed towards a system that achieves approximately 51% reduction in visual display space for numeric data by adopting Gole number patterns, thus reducing pixel usage in user interfaces.

[0042] Another objective of the present disclosure is directed towards a system that provides power-efficient display rendering, particularly beneficial for mobile devices, wearables, and embedded systems, by minimizing the number of pixels activated during numeric data representation.

[0043] Another objective of the present disclosure is directed towards a system that includes a custom encoding standard called BASCII (Bharath Arranged Standard Code for Information Interchange) to represent a comprehensive set of symbols, digits, punctuations, and control characters using a structured and culturally relevant character mapping.

[0044] Another objective of the present disclosure is directed towards a system that supports multi-base numerical representations, enabling the use of base-20, base- 64, base-100, base-128, or other variants depending on the precision and compactness required for specific use cases.

[0045] Another objective of the present disclosure is directed towards a system that leverages sparse data encoding in memory and on display, optimizing both storage and rendering logic to support high-throughput, low-power applications.

[0046] Another objective of the present disclosure is directed towards a system that reduces the display space required for rendering numerical values, thereby enabling more compact user interface layouts and improving overall display efficiency.

[0047] Another objective of the present disclosure is directed towards a system thatminimizes the number of pixels activated on a screen during the display of numerical data, as a direct result of compact visual representations provided by the Gole Number System.

[0048] Another objective of the present disclosure is directed towards a system that achieves reduced power consumption in digital display devices by limiting pixel usage, which is particularly beneficial for battery-powered devices such as smartphones, smartwatches, and loT interfaces.

[0049] Another objective of the present disclosure is directed towards a system that supports high-density information display on limited screen areas, improving readability and data accessibility in space-constrained environments such as wearables and embedded displays.

[0050] Another objective of the present disclosure is directed towards a system that improves data transmission efficiency by representing numerical data in a compact symbolic format, thereby reducing the amount of data transmitted over networks.

[0051] Another objective is directed towards a system that extends the symbolic representation to memory address encoding using a novel base-128 representation scheme, referred to as the Evishta Number System, which allows for high-density address mapping and efficient memory utilization.

[0052] Another objective is directed towards a system that enables hardware and software components to efficiently encode, decode, and display base-128 symbolic data for applications such as low-power memory addressing, embedded computing, and secure data processing.

[0053] According to an exemplary aspect of the present disclosure, a first computing device comprising a processor, a memory, and an interface, wherein the first computing device is configured to execute instructions for symbol-basednumerical processing and rendering through the processor.

[0054] According to another exemplary aspect of the present disclosure, a storage unit operatively coupled to the first computing device, wherein the storage unit comprising a memory array, the memory array comprising a plurality of rows, each row corresponding to a distinct Gole symbol, and a plurality of columns representing positional indexes of digits in numerical sequences, the storage unit configured to store encoded representations of numerical values using a predefined base- 100 symbol set, wherein the base- 100 symbol set comprises 100 uniquely designed Gole symbols, each symbol mapped to a corresponding decimal value from 0 to 99, thereby optimizing memory utilization within the storage unit.

[0055] According to another exemplary aspect of the present disclosure, the processor is configured to receive a numerical input in decimal format, and convert the decimal input into a base- 100 representation, wherein each digit of the base- 100 representation is mapped to a corresponding Gole symbol from the stored symbol set, and the mapped Gole symbols are stored in the memory array according to their respective positions in the numerical sequence, whereby the Gole symbol data is retrieved from the memory array and encoded into a format suitable for display rendering, and the encoded Gole symbols are transmitted to the display unit of the first computing device for visual presentation.

[0056] According to another exemplary aspect of the present disclosure, the display unit is configured to display the Gole symbols using reduced pixel dimensions per character relative to decimal digits, thereby minimizing total pixel usage and reducing the overall power consumption of the display device.BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In the following, numerous specific details are set forth to provide a thorough description of various embodiments. Certain embodiments may be practiced without these specific details or with some variations in detail. In someinstances, certain features are described in less detail so as not to obscure other aspects. The level of detail associated with each of the elements or features should not be construed to qualify the novelty or importance of one feature over the others.

[0058] FIG. 1A is a block diagram depicting a schematic representation of a system for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing, in accordance with one or more exemplary embodiments.

[0059] FIG. IB is an example diagram depicting the prior art of the decimal number representations, in accordance with one or more exemplary embodiments.

[0060] FIG. 2 is an example diagram depicting a sample view of the RNumber system with base 20 numerical representations, in accordance with one or more exemplary embodiments.

[0061] FIG. 3, FIG. 4, and FIG. 5 are example diagrams depicting the RNumber system with base 20 numerical representations, the RNumber system with base 64 numerical representations, and the RNumber system with base 100 numerical representations, in accordance with one or more exemplary embodiments.

[0062] FIG. 6 is an example diagram depicting an optimized hardware memory representation for the RNumber system with base 100, in accordance with one or more exemplary embodiments.

[0063] FIG. 7 is a diagram depicting a Gole number system symbol set, illustrating the mapping of decimal values from 0 to 100 to uniquely designed Gole symbols, in accordance with one or more exemplary embodiments.

[0064] FIG. 8A is a diagram depicting compact symbolic representations of a number, a date, and a time using the Gole number system and Evishta for memoryrepresentation, in accordance with one or more exemplary embodiments.

[0065] FIG. 8B is an example diagram depicting a comparison between a conventional time display format and a compact symbolic time representation using the Gole Number System, in accordance with one or more exemplary embodiments of the present disclosure.

[0066] FIG. 9 is a diagram depicting an extended character mapping structure for the BASCII (Bharath Arranged Standard Code for Information Interchange) system, in accordance with one or more exemplary embodiments.

[0067] FIG. 10 is a diagram depicting a character encoding table for the BASCII (Bharath Arranged Standard Code for Information Interchange) system, mapping decimal ranges to a diverse set of symbolic, control, and alphanumeric characters, including Gole digits, in accordance with one or more exemplary embodiments.

[0068] FIG. 11A is an example diagram depicting a 10-segment display architecture for representing numerals or time values using Gole symbols, in accordance with one or more exemplary embodiments of the present disclosure.

[0069] FIG. 11B, an example diagram 1100b illustrates a Binary to Gole (BCG) conversion table, in accordance with one or more exemplary embodiments of the present disclosure.

[0070] FIG. 12 is a flow diagram depicting a method for using a base- 100 numerical representation system for enhanced data compression and indexing, in accordance with one or more exemplary embodiments.

[0071] FIG. 13 is a flow diagram depicting a method for hardware-driven lowdimensional numerical representation for enhanced data compression and indexing, in accordance with one or more exemplary embodiments.

[0072] FIG. 14 is a block diagram illustrating the details of a digital processing system in which various aspects of the present disclosure are operative by the execution of appropriate software instructions.DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0073] It is to be understood that the present disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The present disclosure is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein are for the purpose of description and should not be regarded as limiting.

[0074] The use of “including”, “comprising” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms “a” and “an” herein do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item. Further, the use of terms “first”, “second”, “third”, and the like, herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another.

[0075] Referring to FIG. 1A is a block diagram 100a depicting a schematic representation of a system for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing, in accordance with one or more exemplary embodiments. The system includes a first computing device 102a, a network interface 104a, a storage unit 106a, an interface 108a, a network 110a, and a second computing device 112a.

[0076] The first computing device 102a may be a primary computing infrastructure where the RNumber system will be implemented. The first computing device 102amay include existing hardware components such as processors, memory modules, and input / output interfaces. The network interface 104a may be configured to provide communication between the first computing device 102a and external networks or devices. The network interface 104a may allow the system 100a to connect to remote resources or exchange data with other computing systems over the network. The storage unit 106a may be configured to store data, software instructions, and configurations relevant to the hardware -driven numerical representation system. The storage unit 106a may include secondary memory devices such as hard drives, flash memory, or cloud-based storage solutions. The interface 108a may be configured to provides a means for interaction between the hardware-driven system and external devices or user interfaces. The interface 108a may be configured to enable the users to input data, configure system settings, or retrieve processed results from the system. The network 110a may Represents the underlying network infrastructure through which data is transmitted between computing devices. The network 110a may include, but not limited to, an Internet of things (loT network devices), an Ethernet, a wireless local area network (WLAN), or a wide area network (WAN), a Bluetooth low energy network, a ZigBee network, a WIFI communication network e.g., the wireless high speed internet, or a combination of networks, a cellular service such as a 4G (e.g., LTE, mobile WiMAX) or 5G cellular data service, a RFID module, a NFC module, wired cables, such as the world-wide-web based Internet, or other types of networks may include Transport Control Protocol / Intemet Protocol (TCP / IP) or device addresses (e.g. network-based MAC addresses, orthose provided in a proprietary networking protocol, such as Modbus TCP, or by using appropriate data feeds to obtain data from various web services, including retrieving XML data from an HTTP address, then traversing the XML for a particular node) and so forth without limiting the scope of the present disclosure. The second computing device 112a may represent additional computing resources that may be integrated into the system to support the hardware-driven numerical representation tasks. These resources can include specialized processing units, dedicated hardware accelerators, or supplementary memory modules.

[0077] In accordance with one or more exemplary embodiments of the present disclosure, the hardware implementation of the system may be achieved through two primary approaches: modifying existing hardware infrastructure or introducing new hardware components to support the existing architecture. This flexibility enables seamless integration of the hardware-driven low-dimensional numerical representation system into diverse computing environments. In the context of modifying existing hardware, adjustments can be made to the configuration and functionality of the current infrastructure to accommodate the requirements of the RNumber system. This may involve reconfiguring memory modules, optimizing processing units, or adapting input / output interfaces to support the efficient encoding and decoding of numerical data using the RNumber framework. By leveraging the existing hardware resources, this approach offers a cost-effective and expedient solution for implementing the system, minimizing the need for extensive hardware upgrades or replacements. Conversely, the introduction of new hardware components can enhance the capabilities and performance of the existing infrastructure to fully leverage the benefits of the RNumber system. This may involve integrating specialized processing units, dedicated memory modules, or custom-built hardware accelerators designed specifically for numerical representation tasks. By augmenting the existing hardware with purpose-built components, the system can achieve unprecedented levels of efficiency, scalability, and processing power, enabling advanced data compression and indexing capabilities.

[0078] In accordance with one or more exemplary embodiments of the present disclosure, the second computing device 112a integrates into the system 100a to augment the computational capabilities required for hardware-driven numerical representation tasks. It provides additional resources such as processing units, memory modules, or specialized hardware components tailored to support the specific requirements of the RNumber system. For instance, the second computing device may handle intensive computational tasks, offload processing from theprimary computing infrastructure, or execute parallelized algorithms to enhance the efficiency of data compression and indexing operations. The network interface 104a serves as a bridge between the first computing device 102a and external networks or devices, facilitating seamless communication and data exchange. It supports various communication protocols and technologies such as Ethernet, Wi-Fi, or cellular data services, depending on the network infrastructure requirements. For example, the network interface may utilize TCP / IP protocols for internet connectivity, Bluetooth for wireless data transmission, or Ethernet for local network connections. By leveraging these communication technologies, the network interface enables the system to access remote resources, exchange data with external devices, and collaborate with distributed computing environments. The storage unit 106a stores diverse types of data, software instructions, and configurations essential for the hardware-driven numerical representation system. This includes numerical datasets, algorithm implementations, and system configurations necessary for efficient data compression and indexing. Additionally, the storage unit may contain metadata, indexing structures, or caching mechanisms to optimize data retrieval and processing performance. By centralizing these resources, the storage unit ensures accessibility, reliability, and scalability of critical data assets required for the effective operation of the hardware-driven numerical representation system. The interface 108a provides a user-friendly means for interacting with the hardware -driven numerical representation system, offering diverse interaction capabilities tailored to user requirements. This includes user input mechanisms, configuration interfaces, and data retrieval methods designed to facilitate seamless interaction with the system. For example, the interface may feature graphical user interfaces (GUIs), command-line interfaces (CLIs), or application programming interfaces (APIs) to accommodate different user preferences and usage scenarios. Users can input data, configure system settings, visualize processed results, and retrieve relevant information through intuitive interaction mechanisms provided by the interface. Modifying existing hardware infrastructure involves adapting the configuration and functionality of current components to meet the requirements of the RNumber system. This may includeoptimizing memory configurations, upgrading processing units, or enhancing input / output interfaces to support efficient numerical data processing. For instance, memory modules can be reconfigured to accommodate the storage and retrieval of low-dimensional numerical representations, while processing units can be optimized to execute specialized algorithms for data compression and indexing tasks. Additionally, input / output interfaces can be upgraded to handle high-speed data transfer and integrate seamlessly with external devices and networks. Introducing new hardware components enhances the capabilities and performance of the existing infrastructure, unlocking new levels of efficiency, scalability, and processing power for the hardware-driven numerical representation system. Specialized processing units, dedicated memory modules, or custom-built hardware accelerators can be integrated to improve data compression and indexing capabilities, enabling faster processing speeds, higher throughput, and reduced latency. By augmenting the existing hardware with purpose-built components, the system achieves enhanced computational efficiency, scalability, and flexibility, empowering advanced data compression and indexing tasks with unparalleled performance and reliability.

[0079] In accordance with one or more exemplary embodiments of the present disclosure, the hardware-driven low-dimensional numerical representation system is depicted in FIG. 1A excels in optimizing memory utilization, power efficiency, and computational performance. The system achieves this optimization through a combination of innovative hardware design and intelligent algorithmic processing. Memory optimization within the system is achieved through efficient data storage and retrieval mechanisms implemented in storage unit 106a. Utilizing advanced storage technologies such as flash memory and cloud-based solutions, the system minimizes memory footprint while ensuring rapid access to critical data elements. Additionally, sophisticated data compression techniques further enhance memory efficiency, allowing the system to store large datasets in compact formats without sacrificing retrieval speed or accuracy. In addition to memory and power optimization, the system excels in optimizing computational performance,leveraging hardware acceleration and parallel processing techniques to maximize computational throughput. The first computing device 102a is equipped with high- performance processors and specialized hardware accelerators, enabling rapid execution of numerical computation tasks with minimal latency. Furthermore, distributed computing architectures leverage the computational capabilities of the second computing device 112a, enabling parallel execution of complex algorithms across multiple processing units for enhanced performance and scalability. By optimizing memory, power, and computational performance simultaneously, the system delivers unparalleled efficiency and scalability in numerical data processing tasks. This comprehensive optimization strategy ensures that the system can handle large-scale datasets with ease while maintaining low latency and high throughput across a wide range of computational workloads. As a result, the system is well- suited for demanding applications in fields such as scientific computing, machine learning, and data analytics, where efficient utilization of computational resources is paramount.

[0080] In accordance with one or more exemplary embodiments of the present disclosure, the first computing device may include the processor 114a, the memory 116a, and the interface 108a. The first computing device 102a may be configured to execute instructions for symbol-based numerical processing and rendering through the processor 114a. The storage unit 106a may be operatively coupled to the first computing device 102a. The storage unit 106a may include the memory array 118a, the memory array may include the plurality of rows, each row corresponding to a distinct Gole symbol, and a plurality of columns representing positional indexes of digits in numerical sequences, the storage unit 106a may be configured to store encoded representations of numerical values using a predefined base- 100 symbol set, and compact memory address representations using an evishta base-128 symbol set, the base-100 symbol set may includelOO uniquely designed Gole symbols, each symbol mapped to a corresponding decimal value from 0 to 99, thereby optimizing memory utilization within the storage unit 106a. The processor 114a may be configured to receive a numerical input in decimal format, and convertthe decimal input into a base- 100 representation using a binary to gole converter (BCG), each digit of the base- 100 representation is mapped to a corresponding Gole symbol from the stored symbol set, and the mapped Gole symbols are stored in the memory array 118a according to their respective positions in the numerical sequence, the Gole symbol data is retrieved from the memory 116a array and encoded into a format suitable for display rendering, and the encoded Gole symbols are transmitted to the display unit 120a of the first computing device 102a for visual presentation, the use of a base- 100 numeral system enables representation of large numerical values using fewer digits compared to decimal systems, thereby reducing data size and improving transmission speed across networked communication environments. The display unit 120a may be configured to display the Gole symbols using reduced pixel dimensions per character relative to decimal digits, thereby minimizing total pixel usage and reducing the overall power consumption of the display device.

[0081] Referring to FIG. IB is an example diagram 100b depicting the prior art of the decimal number representations, in accordance with one or more exemplary embodiments. The diagram 100b highlights the limitations of the decimal number system in efficiently representing large numbers. In the traditional decimal number system, there are 9 unique representations from 1 to 9. However, after reaching the number 9, an additional digit is required to represent the next number. For instance, to represent the number 10, two digits, 1 and 0, are needed. This pattern continues for subsequent numbers, resulting in an increasing number of digits required to represent larger numbers. For example, to represent the number 9999, four digits are needed in the decimal system. This sequential progression of digits poses challenges in terms of memory usage and storage efficiency, particularly when dealing with large datasets and numerical sequences.

[0082] In accordance with one or more exemplary embodiments of the present disclosure, in this traditional system, there are 9 unique representations from 1 to 9. However, after reaching 9, additional digits are required to represent subsequentnumbers. For example, to represent the number 10, two digits (1 and 0) are necessary. This pattern continues, leading to an increasing number of digits needed for larger numbers. For instance, representing 9999 requires 4 digits in the decimal system. This depiction emphasizes the sequential progression of digits and the inherent inefficiencies in memory usage and storage, particularly for larger numerical values.

[0083] In accordance with one or more exemplary embodiments of the present disclosure, it is acknowledged that the term "RNumber" used throughout this document is a placeholder and can be substituted with a more appropriate or descriptive term as deemed necessary. While "RNumber" is utilized to denote the hardware -driven low-dimensional numerical representation system described herein, it is understood that the actual implementation or commercialization of the system may involve the use of a different designation. The term "RNumber" is employed purely for illustrative purposes to represent the overarching concept of the hardware -driven numerical representation system and its associated methodologies for data compression and indexing. As such, it is not intended to limit or constrain the naming conventions that may be adopted in practical applications or implementations of the system. Therefore, while "RNumber" is utilized extensively within this document to refer to the hardware-driven numerical representation system, it is acknowledged that the term is interchangeable and can be modified as necessary to accommodate the preferences and requirements of clients, stakeholders, or end-users. This flexibility allows for seamless integration of the system into diverse environments and ensures coherence with established naming conventions.

[0084] Referring to FIG. 2 is an example diagram 200 depicting a sample view of the RNumber system with base 20 numerical representations, in accordance with one or more exemplary embodiments. The RNumber system is designed to revolutionize numerical representation by employing a base-20 system, offering a more efficient alternative to traditional decimal representations. In this exemplarydiagram, the RNumber system with base 20 showcases a streamlined approach to representing numbers, where each digit can represent a larger range of values compared to the decimal system. Unlike the decimal system, which requires additional digits beyond 9 to represent higher numbers, the base-20 RNumber system maintains a consistent representation pattern up to the 20th digit. By utilizing a base-20 numerical representation, the RNumber system reduces the overall number of digits needed to represent large numbers and sequences, leading to enhanced memory efficiency and storage optimization. This innovative approach addresses the limitations of traditional numerical representation systems and offers a more scalable and versatile solution for various applications. Figure 2 provides a visual demonstration of the RNumber system with base 20 numerical representations, highlighting its potential to revolutionize numerical representation and optimize memory usage in accordance with exemplary embodiments.

[0085] Referring to FIG. 3, FIG. 4, FIG. 5, are example diagrams 300, 400, and 500 depicting the RNumber system with base 20 numerical representations, the RNumber system with base 64 numerical representations, and the RNumber system with base 100 numerical representations, in accordance with one or more exemplary embodiments.

[0086] The diagram 300, the RNumber system with base 20 showcases a numerical representation scheme where each digit can represent a range of values from 0 to 19. This base-20 system allows for a more compact representation of numbers, reducing the number of digits needed to represent large numerical values. In this system, each digit can represent a range of values from 0 to 19. The base-20 numerical system offers a more compact representation of numbers compared to traditional systems. For example, to represent the number 9999, which would require 4 digits in the decimal system, only 2 digits are needed in the base-20 RNumber system. This reduction in the number of digits required for numerical representation leads to significant memory optimization and storage efficiency. The diagram 400 may illustrate the RNumber system with base 64 numericalrepresentations, where each digit can represent a range of values from 0 to 63. By utilizing a base-64 numerical system, the RNumber system further expands the range of representable values while maintaining a compact representation format. In this system, each digit can represent a range of values from 0 to 63. By utilizing a base-64 numerical system, the RNumber system expands the range of representable values while maintaining a compact representation format. This allows for the efficient encoding of large numbers and sequences with minimal digits, leading to enhanced memory optimization and storage efficiency. The diagram 500, the RNumber system with base 100 numerical representations are presented, wherein each digit can represent a range of values from 0 to 99. This base- 100 system offers even greater flexibility and precision in numerical representation, allowing for the efficient encoding of large numbers and sequences with minimal digits. In this system, there are 99 unique representations, and only two digits are needed after the 99th number. For example, to represent the number 9999, only 2 digits are required in the base- 100 RNumber system. Experimental results indicate that the introduction of the RNumber system with base 100 reduces the numerical representation requirement by 50% compared to conventional systems. This optimization of representing large numbers in fewer digits leads to significant memory optimization and power efficiency. Additionally, the sparse data stored in the base- 100 system further enhances memory optimization, as fewer memory resources are required to represent the same numerical values compared to conventional systems. These exemplary diagrams highlight the versatility and scalability of the RNumber system across different base values, demonstrating its potential to revolutionize numerical representation and optimize memory usage in various applications. The RNumber system offers a compelling solution for efficient and effective numerical representation, paving the way for enhanced data storage and processing capabilities.

[0087] Referring to FIG. 6 is an example diagram 600 depicting an optimized hardware memory representation for the RNumber system with base 100, in accordance with one or more exemplary embodiments. In the RNumber system withbase 100, there are 99 unique representations, and only two digits are needed after the 99th number. This means that even for large numbers like 9999, only 2 digits are required for representation, significantly reducing the memory footprint compared to conventional systems. Experimental results indicate that the introduction of the RNumber system with base 100 reduces the numerical representation requirement by 50% compared to traditional decimal systems. To further optimize memory usage, an array of memory is allocated consisting of rows and columns during hardware implementation. Each symbol from the proposed representation is allocated a row, resulting in 99 rows in the memory. The column size may vary depending on the amount of data intended to be stored, allowing for flexibility and efficient utilization of memory resources. The binary representation of numbers in the RNumber system with base 100 showcases the optimization achieved through numerical representation and hardware memory implementation. For example, the decimal number 969899 is efficiently represented using only three l's in the base- 100 system, whereas conventional memory hardware would require 12 l's. This optimization not only reduces memory usage but also contributes to power efficiency, as fewer memory resources are needed for the same numerical values compared to conventional systems.

[0088] In accordance with one or more exemplary embodiments of the present disclosure, In the RNumber system with base 100, the representation of numbers is streamlined to utilize only two digits after the 99th number, significantly reducing the memory requirement for storing large numerical values. For instance, to represent the number 9999, only 2 digits are needed, whereas conventional systems would require four digits. Experimental findings underscore the remarkable efficiency achieved by the RNumber system with base 100, indicating a 50% reduction in numerical representation requirements compared to traditional decimal systems. This optimization ensures that even extensive numerical sequences can be efficiently stored and processed with minimal memory usage. The hardware implementation of the RNumber system leverages an array-based memory structure, featuring rows and columns. Each symbol in the numerical representationis allocated a dedicated row within the memory array. Consequently, the memory array comprises 99 rows, accommodating the unique representations of the base- 100 system. Flexibility is a key aspect of the hardware memory implementation, allowing the column size to vary based on the intended data storage requirements. This adaptability ensures optimal utilization of memory resources across diverse applications and datasets. The binary representation of numbers in the RNumber system with base 100 exemplifies the efficiency gained through numerical representation and hardware memory optimization. For instance, the decimal number 969899 is efficiently encoded using only three l's in the base- 100 system, compared to the twelve l's required by conventional memory hardware. This reduction in memory usage not only enhances storage efficiency but also contributes to power optimization, as fewer memory resources are needed to represent the same numerical values.

[0089] Referring to FIG. 7 is a diagram 700 depicting a Gole number system symbol set, illustrating the mapping of decimal values from 0 to 100 to uniquely designed Gole symbols, in accordance with one or more exemplary embodiments. The diagram maps decimal values from 0 to 100 to corresponding visually distinct Gole symbols, arranged in a clear tabular format. The first row of the table displays decimal values (e.g., 0, 1, 2, ..., 100), while the second row displays the associated Gole symbols. These symbols have been custom-designed to be compact, distinct, and visually suitable for both digital display and symbolic computation. The symbol set includes curves and strokes optimized for minimal space usage on digital screens. The Gole symbols allow for numerical values such as 384400 to be represented using only three unique Gole digits, significantly reducing the number of characters required. This contributes to reduced memory allocation, display size, and power consumption. The system not only reduces symbolic length but also enhances display performance. Due to the compactness and uniform height of Gole symbols, pixel utilization on display screens is minimized, contributing to power efficiency a critical factor in mobile, embedded, and loT systems. This standardized Gole symbol set forms the foundation for the base- 100 Gole Number System, whichis compatible with both hardware -level memory encoding and software-based compression systems. The symbols may be stored in firmware, embedded font libraries, or used in conjunction with the BASCII encoding scheme for efficient rendering and processing.

[0090] In accordance with one or more exemplary embodiments of the present disclosure, the system introduces a set of 100 uniquely designed symbols, each corresponding to a decimal value from 0 to 99, with an optional extension to include the value 100. The figure is structured in a grid format, where each decimal number is mapped to a custom-designed symbol, collectively referred to as Gole digits. These symbols may be optimized for both visual clarity and spatial compactness, making them particularly suitable for systems where display space, memory, or power consumption may be constrained. The Gole Number System may serve as a direct evolution of the RNumber concept, with FIG. 7 representing its finalized symbol set. Each glyph in the table may be carefully constructed to ensure uniqueness, minimal visual footprint, and compatibility with low-resolution rendering environments. The design inspiration for the Gole symbols may draw from traditional Indian scripts and regional aesthetics to promote intuitive readability while allowing for technological flexibility across font engines and rendering platforms. The Gole number system may be employed to represent large numerical values using significantly fewer digits than conventional decimal systems. For example, a number like 384400, which would require six digits in base- 10, may be encoded using only three Gole digits. This reduction in the number of symbols may translate directly into reduced screen space usage and fewer activated pixels, which in turn may lead to lower power consumption an important advantage in battery-powered or embedded computing environments. The symbols shown in FIG. 7 may be intended for integration into both software and hardware implementations. On the software side, they may be stored as a custom font or Unicode-compatible private use area, allowing them to be displayed in user interfaces, mobile applications, or digital dashboards. On the hardware side, these symbols may be encoded directly into memory using associated binary values, andmay be processed using specialized rendering logic in microcontrollers, digital displays, or smart sensors. The compact and consistent shape of the Gole symbols may enable high-density information visualization, making them particularly suitable for environments with limited screen real estate, such as wearables, smart badges, loT dashboards, or public signage. In combination with other encoding schemes such as the proposed BASCII standard, these symbols may be part of a larger ecosystem for culturally resonant, compact, and efficient information representation. The Gole Number System may be described as an evolved version of the previously introduced RNumber concept, specifically implemented using a base- 100 numerical representation. While the RNumber system laid the foundation for low-dimensional number encoding, the Gole Number System advances this idea by introducing a complete set of 100 uniquely designed symbols, allowing for the compact representation of large numerical values with minimal digits. This evolution is not limited to symbolic compression but also extends to hardware efficiency, visual display optimization, and practical usability. By leveraging a higher base and a custom symbol set, the Gole Number System may offer improved scalability, better integration into display devices, and enhanced adaptability across various computational platforms, including memory-constrained, power-sensitive, and display-limited environments. In summary, FIG. 7 provides the visual foundation of the Gole Number System’s symbolic structure. These symbols may form the basis of a patentable and scalable number representation system that not only reduces symbolic length and visual size but also supports efficiency in memory, computation, display output, and energy consumption across various digital systems and devices.

[0091] Referring to FIG. 8A is a diagram 800a depicting compact symbolic representations of a number, a date, and a time using the Gole number system and Evishta for memory representation, in accordance with one or more exemplary embodiments. The diagram illustrates practical examples of how the Gole Number System may be used to represent conventional numerical data specifically a numeric value, a calendar date, and a time of day using the custom base- 100symbolic format. These representations may highlight the real-world utility of the Gole Number System for display compression, readability, and storage efficiency. In the first row of FIG. 8A, the number 384400 is shown as being converted into a three-symbol Gole representation. While this number would typically require six characters in the decimal system, the Gole encoding reduces it to only three characters. This reduction may result from the system’s ability to express a wider range of values per digit due to its base- 100 nature. The visual footprint of this representation may be reduced by more than 50%, which may directly impact display layout efficiency and rendering performance in devices with limited screen size. The second row of the figure illustrates a date conversion, where the date 23- 11-2013 is represented as a compact sequence of four Gole digits. In this format, each component (day, month, and year segments) may be individually encoded using Gole symbols, with separators or delimiters optionally included as part of the display standard. This example shows how the Gole Number System may be adapted to work with structured or segmented data formats, while preserving their integrity and improving space usage. The third row shows the conversion of a time value, specifically 10:38, into its corresponding Gole representation. Similar to the date format, the time components may be encoded using one or two Gole digits each, with a visual delimiter retained to maintain readability. This transformation illustrates how temporal data may be compressed and simplified without loss of interpretability. The examples in FIG. 8A demonstrate a powerful application of the Gole Number System in UI / UX optimization, particularly in digital clocks, status panels, smartwatches, dashboards, and display panels where screen real estate is limited. Additionally, such compact symbolic representations may result in reduced pixel rendering requirements, contributing to lower power consumption, which may be critical in battery-operated devices. These patterns may be part of a standardized approach for rendering numerical, date, and time data using the Gole system, and may also be extended into other formats such as IP addresses, identification numbers, geocoordinates, or encoded metadata. As such, the Gole patterns shown in this figure may offer a unified, compressed, and power-efficient method for presenting structured information across a wide range of computing systems.

[0092] Referring to FIG. 8B is an example diagram 800b depicting a comparison between a conventional time display format and a compact symbolic time representation using the Gole Number System, in accordance with one or more exemplary embodiments of the present disclosure. The diagram 800b depicts a wearable device or smart watch having a display screen 802B that shows the time " 10:38" in a traditional decimal representation. In contrast, display screen 804B illustrates the same time information " 10:38" represented using Gole symbols derived from the base- 100 numeral system. The compact symbolic representation not only reduces the number of pixels required for rendering the time but also significantly minimizes the visual footprint on the display. The visual footprint of this representation may be reduced due to the inherently compact structure of Gole symbols, which are designed to occupy lesser pixel dimensions compared to conventional decimal digits. This reduced visual footprint may lead to optimized space utilization on small screens, such as smart watches or loT displays, thereby enabling clearer display layouts and lower power consumption for rendering time information. The compact symbolic representations may be advantageous in scenarios where screen space is limited, or power efficiency is a critical requirement, allowing devices to display more information within constrained display areas without compromising on readability or design aesthetics.

[0093] Referring to FIG. 9 is a diagram 900 depicting an extended character mapping structure for the BASCII (Bharath Arranged Standard Code for Information Interchange) system, in accordance with one or more exemplary embodiments, which integrates the Gole Number System with extended symbolic representation for digital data processing and display. The table maps specific decimal ranges to categories of characters used in numeric, textual, and symbolic encoding. The decimal ranges from 0 to 99 is exclusively reserved for Gole Digits, which serve as the primary representation format in the base- 100 Gole Number System. These digits are uniquely designed and optimized for compact display, memory efficiency, and high-speed encoding operations. The Gole digits occupythe foundational segment of the BASCII code, ensuring seamless alignment with hardware encoding schemes and display logic. The subsequent range from 100 to 125 is designated for uppercase English alphabets (A-Z). This integration enables the encoding system to support textual data, identifiers, and programming constructs, while maintaining uniformity with conventional character sets. The inclusion of uppercase alphabets expands the applicability of the BASCII system beyond numeric representation, allowing it to function as a complete textual encoding standard. The range from 126 to 127 is allocated to two unique special characters. These symbols may be custom-designed to serve as functional operators, flags, or control codes within the BASCII framework. Their distinct appearance and limited range position them for specialized uses such as logical quantifiers, metadata tags, or system-level identifiers. FIG. 9 thus illustrates a compact and extensible encoding strategy that blends numerals, alphabets, and custom symbols in a unified structure. This design is intended for low-footprint hardware implementations, compact display systems, firmware-level encoding tables, and resource-constrained embedded systems. It enables high-speed processing and efficient memory utilization while maintaining human-readable symbolic formats.

[0094] Referring to FIG. 10 is a diagram 1000 depicting a character encoding table for the BASCII (Bharath Arranged Standard Code for Information Interchange) system, mapping decimal ranges to a diverse set of symbolic, control, and alphanumeric characters, including Gole digits, in accordance with one or more exemplary embodiments. The decimal range 0-99 is exclusively reserved for the core Gole Digits, which form the foundation of the base- 100 numerical representation system. This ensures maximum compatibility with Gole-based compression and memory optimization. The subsequent range from 100-125 is allocated to uppercase alphabetic characters A-Z, supporting text display and programming syntax. The range from 126-127 is reserved for two additional custom symbols (a stylized representation for specialized symbolic use). The extended ranges from 128-133 and 134-140 include various punctuation and mathematical operators respectively. These comprise commonly used characterssuch as comma, period, equals, angle brackets, exclamation mark, plus, minus, asterisk, division, parentheses, and caret symbols. These are followed by additional symbols between 141-148 including slash, percent, colon, semicolon, question mark, quotation marks, and backslash which are frequently used in structured documents, code, and data formatting. The 149-153 range accommodates general- purpose symbols such as the at-sign (@), underscore (_), hash (#), pipe, and ampersand (&), allowing for integration with scripting languages, command structures, and markup syntax. Control characters including the space and newline are assigned to the 154-155 range for text parsing, layout, and communication formatting. Notably, the 156-181 range is dedicated to lowercase alphabet characters (a-z), completing full support for case-sensitive alphabetic encoding. The final range of 182-186 includes essential structural symbols such as square brackets [ ], curly braces { }, and the tab character facilitating structured code, data organization, and display formatting. The BASCII system presented in FIG. 10 provides a unified framework for encoding numeric, symbolic, and alphabetic information within hardware or software systems. It enables smooth transition between Gole digits and textual representations within the same encoding framework. The structure is particularly suitable for embedded systems, low-power devices, display rendering engines, and compact memory architectures. This unified and extended encoding table may also improve interoperability in data communication protocols and enhance storage compression algorithms.

[0095] In accordance with one or more exemplary embodiments of the present disclosure, the compact symbolic representation of numerical data using the base- 100 Gole Number System contributes not only to memory and display optimization, but also to enhanced data transmission efficiency. By reducing the number of digits required to encode large numerical values, the system minimizes the volume of data transmitted over communication networks, thereby improving transmission speed and lowering bandwidth consumption across networked devices. In addition to data compression and display rendering, the present disclosure further introduces an extended symbolic representation format known as the Evishta Number System,which employs a base-128 structure to represent memory addresses in a compact and structured format. Much like hexadecimal serves as an extended form of decimal (base- 16), Evishta is designed as an expanded variant of the Gole Number System, optimized for encoding high-density address values in computing systems. To support this extended range of symbolic representation, BASCII (Bharath Arranged Standard Code for Information Interchange) has first 100 characters as Gole symbols and next 26 as upper-case A-Z and next 2 as special symbols. This way order of 128 symbols is preserved for Evishta number system, the character encoding table is also disclosed, which integrates the new Evishta symbols alongside the existing Gole symbols, control characters, and alphanumeric ranges. This BASCII table enables consistent encoding, decoding, and interoperability between Gole-based numerical representations and Evishta-based memory operations within a unified symbolic framework, supporting a wide range of applications including memory mapping, data communication, embedded systems, and symbolic compression in digital environments.

[0096] In accordance with one or more exemplary embodiments of the present disclosure, the specific graphical forms and design characteristics of the Gole and Evishta symbols are not intended to be limited to a fixed set. The symbols used in the base-100 and base-128 numerical representation systems may be customized, redefined, or extended based on visual clarity, application-specific requirements, display constraints, or cultural preferences. These symbol sets may evolve over time to accommodate improvements in symbol recognition, digital aesthetics, or font rendering technologies. The underlying logic of mapping each symbol to a unique numerical value within the respective base system remains consistent, regardless of the symbol’s visual form. This adaptability ensures that the symbolic number system remains compatible with a wide range of digital environments, user interfaces, and character encoding standards such as BASCII, while preserving the intended benefits of compact numerical representation, memory optimization, and communication efficiency.

[0097] Referring to FIG. 11A is an example diagram 1100a depicting a 10-segment display architecture for representing numerals or time values using Gole symbols, in accordance with one or more exemplary embodiments of the present disclosure. 10-segment display layout that may be utilized for displaying numerical values, time information, or symbols encoded in the Gole Number System. The display architecture comprises a plurality of segments, including atop segment 1102a, side segments 1104a, 1106a, 1108a, 1114a, 1116a, 1118a, middle segments 1110a, 1112a, and a bottom segment 1120a. The Gole Number System may be adaptable for use in segment-based display technologies, such as 10-segment, or 12-segment displays. Specifically, a Binary to Gole Conversion (BCG) mechanism may be employed to convert standard binary or decimal input values into corresponding Gole symbols suitable for segment display rendering. The segment configuration illustrated in FIG. 11A may enable the accurate and compact representation of Gole symbols using a minimal number of active display segments. This approach ensures compatibility of the Gole Number System with conventional segment-based display units while allowing for enhanced data compression, visual compactness, and power optimization. The segment-based Gole symbol rendering may be particularly advantageous in low-power devices, wearable electronics, smart watches, loT displays, and embedded systems where display area and energy consumption are critical design considerations. The BCG (Binary to Gole Converter) may facilitate seamless integration of this representation approach within both new and existing hardware implementations.

[0098] Referring to FIG. 11B, an example diagram 1100b illustrates a Binary to Gole (BCG) conversion table, in accordance with one or more exemplary embodiments of the present disclosure, which may provide a mapping between binary code patterns and corresponding Gole digits. The BCG conversion may follow a concept similar to the conventional Binary Coded Decimal (BCD) representation used in digital systems, wherein binary values are mapped to human- readable decimal digits. In the present disclosure, the BCG conversion is adapted specifically for the Gole Number System to facilitate compact and efficientencoding and decoding of numerical data within embedded systems. In the BCG conversion, each binary code pattern may be mapped to a corresponding Gole digit ranging from 0 to 99. The binary code may be represented using a fixed number of bits, such as 7-bit or 8-bit encoding, depending on the system design or hardware requirements. However, the number of bits used is not limited to this and may vary based on implementation needs. By utilizing this BCG conversion approach, it becomes easier to encode and decode Gole symbols in embedded systems or hardware-driven environments. For instance, binary input data generated from memory or processing units may be directly converted into Gole symbols for display on segment-based displays or for further symbolic representation. This method of conversion ensures compatibility with existing binary processing architectures while retaining the advantages of the Gole Number System for compact data representation. Furthermore, the BCG conversion enables efficient handling of numerical data in applications such as embedded systems, loT devices, wearable electronics, or any system where low-dimensional number representation, optimized display, and power efficiency are critical. The BCG encoding and decoding process may be implemented in hardware or software modules within the embedded system, enabling seamless conversion between binary data and Gole symbols without adding significant complexity to the system design.

[0099] Referring to FIG. 12 is a flow diagram 1200 depicting a method for using a base- 100 numerical representation system for enhanced data compression and indexing, in accordance with one or more exemplary embodiments. The method commences at step 1202, providing an RNumber with base 100 numerical representations using 99 unique representations. Thereafter at step 1204, generating numerical sequences and values using the base- 100 numerical representation system. Thereafter at step 1206, allocating memory resources in a computing hardware implementation. Thereafter at step 1208, adding blocks for read memory and write memory to facilitate efficient read and write operations within the computing hardware implementation. Thereafter at step 1210, adjusting the column size of the memory array based on the intended data storage requirements.Thereafter at step 1212, encoding numerical values into binary representations within the RNumber with base 100 numerical representations.

[0100] Referring to FIG. 13 is a flow diagram 1300 depicting a method for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing, in accordance with one or more exemplary embodiments. The method commences at step 1302, receiving a numerical input in decimal format by a processor of a computing device and converting the decimal input into a base-100 representation. Thereafter at step 1304, mapping each digit of the base- 100 representation to a corresponding Gole symbol from a predefined symbol set comprising 100 uniquely designed symbols, each symbol mapped to a decimal value from 0 to 99. Thereafter at step 1306, storing the mapped Gole symbols in a memory array within a storage unit, wherein the memory array comprises a plurality of rows corresponding to the Gole symbols and a plurality of columns representing digit positions, thereby optimizing memory utilization within the storage unit. Thereafter at step 1308, retrieving the stored Gole symbols from the memory array and encoding them into a format suitable for display rendering. Thereafter at step 1310, displaying the encoded Gole symbols on a display unit using reduced pixel dimensions per character relative to decimal digits, thereby minimizing total pixel usage and reducing overall power consumption of the display device.

[0101] In accordance with one or more exemplary embodiments of the present disclosure, all samples, calculations, and diagrams provided herein are exemplary. These representations serve to illustrate the principles and functionalities of the hardware-driven low-dimensional numerical representation system described in this document. While the examples presented demonstrate the capabilities and potential applications of the system, they are not exhaustive and may not encompass all possible scenarios or implementations. The samples included in this document are intended to showcase the versatility and effectiveness of the system across various use cases and datasets. They may depict simplified orhypothetical scenarios to aid in understanding the underlying concepts and methodologies employed by the system. Similarly, the calculations presented are illustrative of the computational techniques and algorithms utilized for numerical data processing, compression, and indexing within the system. The diagrams provided offer visual representations of the system architecture, components, and data flow, allowing for easier comprehension of the system's structure and operation. These diagrams are designed to highlight key aspects of the hardware- driven numerical representation system, including its integration with existing computing infrastructure, data storage mechanisms, and network connectivity. It is essential to recognize that while the examples, calculations, and diagrams presented herein are based on real-world scenarios and implementations, they are intended for illustrative purposes only. Actual implementations of the system may vary depending on specific requirements, hardware configurations, and application domains. Therefore, readers are encouraged to interpret the information provided in this document as guiding principles rather than rigid specifications, adapting them to suit their individual needs and circumstances.

[0102] In accordance with one or more exemplary embodiments of the present disclosure, the Gole symbols are stored in a predefined symbol table embedded within the memory of the first computing device, the symbol table being accessible by the processor to perform fast and consistent mapping between decimal values and corresponding Gole symbols during encoding and decoding operations.

[0103] In accordance with one or more exemplary embodiments of the present disclosure, the memory array is implemented using a sparse matrix structure, wherein only active positions corresponding to non-zero or valid numerical values are allocated memory space, thereby reducing unused memory allocation, conserving storage resources, and enhancing data compression efficiency within the system.

[0104] In accordance with one or more exemplary embodiments of thepresent disclosure, the processor is configured to convert structured input data comprising calendar dates and time values into equivalent base- 100 representations using compact Gole symbols, thereby enabling symbolic compression of commonly used date-time information while maintaining readability and display uniformity.

[0105] In accordance with one or more exemplary embodiments of the present disclosure, the display unit is configured to visually present numerical values, calendar dates, and time formats using compressed Gole symbol patterns arranged in a compact visual layout, thereby reducing the occupied screen area required for data presentation and improving display utilization efficiency.

[0106] In accordance with one or more exemplary embodiments of the present disclosure, the display unit is implemented as a low-power digital screen, and wherein the rendering of Gole symbols using reduced pixel dimensions per character contributes to minimized pixel activation, thereby extending battery life and reducing the energy consumption of the device.

[0107] In accordance with one or more exemplary embodiments of the present disclosure, the first computing device is configured to perform encoding and decoding of Gole symbols using a character encoding scheme known as Bharath Arranged Standard Code for Information Interchange (BASCII), the scheme being adapted to support Gole symbols along with standard alphanumeric and control characters.

[0108] In accordance with one or more exemplary embodiments of the present disclosure, the base- 100 Gole symbol representation is dynamically extendable to support additional base configurations including base-20, base-64, and base-128 for compact memory address representation, the selection of base configuration being determined based on application requirements, user preferences, or system resource constraints to allow flexible adaptation of symbol encoding depth.

[0109] In accordance with one or more exemplary embodiments of the present disclosure, the first computing device is communicatively connected to a network interface, the network interface configured to enable data exchange between the first computing device and at least one second computing device over a network.

[0110] Referring to FIG. 14 is a block diagram illustrating the details of digital processing system 1400 in which various aspects of the present disclosure are operative by execution of appropriate software instructions. Digital processing system 1300 may correspond to first and second communication devices (or any other system in which the various features disclosed above can be implemented).

[0111] Digital processing system 1400 may contain one or more processors such as a central processing unit (CPU) 1410, random access memory (RAM) 1420, secondary memory 1427, graphics controller 1460, display unit 1470, network interface 1480, and an input interface 1490. All the components except display unit 1470 may communicate with each other over communication path 1450, which may contain several buses as is well known in the relevant arts. The components of Figure 14 are described below in further detail.

[0112] CPU 1410 may execute instructions stored in RAM 1420 to provide several features of the present disclosure. CPU 1410 may contain multiple processing units, with each processing unit potentially being designed for a specific task. Alternatively, CPU 1410 may contain only a single general-purpose processing unit.

[0113] RAM 1420 may receive instructions from secondary memory 1430 using communication path 1450. RAM 1420 is shown currently containing software instructions, such as those used in threads and stacks, constituting shared environment 1325 and / or user programs 1426. Shared environment 1425 includesoperating systems, device drivers, virtual machines, etc., which provide a (common) run time environment for execution of user programs 1426.

[0114] Graphics controller 1460 generates display signals (e.g., in RGB format) to display unit 1470 based on data / instructions received from CPU 1410. Display unit 1470 contains a display screen to display the images defined by the display signals. Input interface 1490 may correspond to a keyboard and a pointing device (e.g., touch-pad, mouse) and may be used to provide inputs. Network interface 1480 provides connectivity to a network (e.g., using Internet Protocol), and may be used to communicate with other systems (such as those shown in Figure 1A, network) connected to the network.

[0115] Secondary memory 1430 may contain hard drive 1435, flash memory 1436, and removable storage drive 1437. Secondary memory 1430 may store the data software instructions (e.g., for performing the actions noted above with respect to the Figures), which enable digital processing system 1400 to provide several features in accordance with the present disclosure.

[0116] Some or all of the data and instructions may be provided on the removable storage unit 1440, and the data and instructions may be read and provided by removable storage drive 1437 to CPU 1410. Floppy drive, magnetic tape drive, CD-ROM drive, DVD Drive, Flash memory, a removable memory chip (PCMCIA Card, EEPROM) are examples of such removable storage drive 1437.

[0117] The removable storage unit 1440 may be implemented using medium and storage format compatible with removable storage drive 1437 such that removable storage drive 1437 can read the data and instructions. Thus, removable storage unit 1440 includes a computer readable (storage) medium having stored therein computer software and / or data. However, the computer (or machine, in general) readable medium can be in other forms (e.g., non-removable, random access, etc.).

[0118] In this document, the term "computer program product" is used to generally refer to the removable storage unit 1440 or hard disk installed in hard drive 1435. These computer program products are means for providing software to digital processing system 1300. CPU 1410 may retrieve the software instructions, and execute the instructions to provide various features of the present disclosure described above.

[0119] The term “storage media / medium” as used herein refers to any non- transitory media that store data and / or instructions that cause a machine to operate in a specific fashion. Such storage media may comprise non-volatile media and / or volatile media. Non-volatile media includes, for example, optical disks, magnetic disks, or solid-state drives, such as storage memory 1430. Volatile media includes dynamic memory, such as RAM 1420. Common forms of storage media include, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, NVRAM, any other memory chip or cartridge.

[0120] Storage media is distinct from but may be used in conjunction with transmission media. Transmission media participates in transferring information between storage media. For example, transmission media includes coaxial cables, copper wire and fiber optics, including the wires that comprise bus 850. Transmission media can also take the form of acoustic or light waves, such as those generated during radio-wave and infra-red data communications.

[0121] The storage device 1495 may be an "Additional Device," which augments the system's capabilities and functionality. The storage device 1495 serves as an auxiliary computing and storage unit, supplementing the primary processing resources provided by CPU 1310, RAM 1320, and secondary memory1330. The inclusion of this separate computing / storage device 1395 underscores its role in enhancing computational performance and expanding data storage capacity within the digital processing system 1400. The presence storage device 1495 enriches the overall system infrastructure, facilitating improved efficiency, scalability, and flexibility in executing software instructions and managing data storage operations. Furthermore, the enhanced system architecture underscores the adaptability and extensibility of the digital processing system 1400, enabling seamless integration of additional computing resources to meet evolving computational demands and application scenarios. With the inclusion of the additional computing / storage device 1495, the digital processing system 1400 gains access to expanded computational resources and storage capacity, fostering enhanced performance and capability across various computing tasks and applications. The storage device 1495 enriches the functional spectrum of the system, empowering it to tackle complex computational challenges and data- intensive processing workloads with greater ease and efficiency. Moreover, the expanded functional spectrum enables the digital processing system 1400 to support a broader range of applications and use cases, from real-time data analytics to high- performance computing tasks, thereby amplifying its utility and value in diverse computing environments.

[0122] Reference throughout this specification to “one embodiment”, “an embodiment”, or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Thus, appearances of the phrases “in one embodiment”, “in an embodiment” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

[0123] Although the present disclosure has been described in terms of certain preferred embodiments and illustrations thereof, other embodiments and modifications to preferred embodiments may be possible that are within the principles of the invention. The above descriptions and figures are therefore to beregarded as illustrative and not restrictive.

[0124] Thus, the scope of the present disclosure is defined by the appended claims and includes both combinations and sub-combinations of the various features described hereinabove as well as variations and modifications thereof, which would occur to persons skilled in the art upon reading the foregoing description.

Claims

CLAIMS1. A system for hardware-driven low-dimensional numerical representation for enhanced data compression and indexing, comprising: a first computing device comprising a processor, a memory, and an interface, wherein the first computing device configured to execute instructions for symbol-based numerical processing and rendering through the processor; a storage unit operatively coupled to the first computing device, wherein the storage unit comprising a memory array, the memory array comprising a plurality of rows, each row corresponding to a distinct Gole symbol, and a plurality of columns representing positional indexes of digits in numerical sequences, the storage unit configured to store encoded representations of numerical values using a predefined base- 100 symbol set, and compact memory address representations using an evishta base- 128 symbol set, wherein the base- 100 symbol set comprises 100 uniquely designed Gole symbols, each symbol mapped to a corresponding decimal value from 0 to 99, thereby optimizing memory utilization within the storage unit; the processor is configured to receive a numerical input in decimal format, and convert the decimal input into a base- 100 representation using a binary to gole converter (BCG), wherein each digit of the base- 100 representation is mapped to a corresponding Gole symbol from the stored symbol set, and the mapped Gole symbols are stored in the memory array according to their respective positions in the numerical sequence, whereby the Gole symbol data is retrieved from the memory array and encoded into a format suitable for display rendering, and the encoded Gole symbols are transmitted to a display unit of the first computing device for visual presentation, wherein the use of a base- 100 numeral system enables representation of large numerical values using fewer digits compared to decimal systems, thereby reducing data size and improvingtransmission speed across networked communication environments; and the display unit is configured to display the Gole symbols using reduced pixel dimensions per character relative to decimal digits, thereby minimizing total pixel usage and reducing the overall power consumption of the display device.

2. The system as claimed in claim 1, wherein the Gole symbols are stored in a predefined symbol table embedded within the memory of the first computing device, the symbol table being accessible by the processor to perform fast and consistent mapping between decimal values and corresponding Gole symbols during encoding and decoding operations.

3. The system as claimed in claim 1, wherein the memory array is implemented using a sparse matrix structure, wherein only active positions corresponding to non-zero or valid numerical values are allocated memory space, thereby reducing unused memory allocation, conserving storage resources, and enhancing data compression efficiency within the system.

4. The system as claimed in claim 1, wherein the processor is configured to convert structured input data comprising calendar dates and time values into equivalent base- 100 representations using compact Gole symbols, thereby enabling symbolic compression of commonly used date-time information while maintaining readability and display uniformity.

5. The system as claimed in claim 1, wherein the display unit is configured to visually present numerical values, calendar dates, and time formats using compressed Gole symbol patterns arranged in a compact visual layout, thereby reducing the occupied screen area required for data presentation and improving display utilization efficiency.

6. The system as claimed in claim 1, wherein the display unit is implemented as a low-power digital screen, and wherein the rendering of Gole symbols using reduced pixel dimensions per character contributes to minimized pixel activation, thereby extending battery life and reducing the energy consumption of the device.

7. The system as claimed in claim 1 , wherein the first computing device is configured to perform encoding and decoding of Gole symbols using a character encoding scheme known as Bharath Arranged Standard Code for Information Interchange (B ASCII), the scheme being adapted to support Gole symbols along with standard alphanumeric and control characters.

8. The system as claimed in claim 1, wherein the base- 100 Gole symbol representation is dynamically extendable to support additional base configurations including base- 20, base-64, and base- 128 for compact memory address representation, the selection of base configuration being determined based on application requirements, user preferences, or system resource constraints to allow flexible adaptation of symbol encoding depth.

9. The system as claimed in claim 1, wherein the first computing device is communicatively connected to a network interface, the network interface configured to enable data exchange between the first computing device and at least one second computing device over a network.

10. A method for hardware- driven low-dimensional numerical representation for enhanced data compression and indexing, the method comprising: receiving a numerical input in decimal format by a processor of a computing device, and converting the decimal input into a base- 100 representation using a Binary to Gole Converter (BCG); mapping each digit of the base- 100 representation to a corresponding Gole symbol from a predefined symbol set comprising 100 uniquely designedsymbols, each symbol mapped to a decimal value from 0 to 99; storing the mapped Gole symbols in a memory array within a storage unit, wherein the memory array comprises a plurality of rows corresponding to the Gole symbols and a plurality of columns representing digit positions, thereby optimizing memory utilization within the storage unit; retrieving the stored Gole symbols from the memory array and encoding them into a format suitable for display rendering; and displaying the encoded Gole symbols on a display unit using reduced pixel dimensions per character relative to decimal digits, thereby minimizing total pixel usage and reducing overall power consumption of the display device.

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