Stochastic Binary String Generators for Accurate Shorter Multiplication
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Solution Overview
Problem
Current stochastic binary string (SBS) representations for computational operations require large string lengths to achieve accurate multiplication, leading to inefficient storage and hardware usage, especially for large values, and existing generators like the ρ-sequence method suffer from inaccuracies and the need for pseudo-random number generators.
Innovation Solution
The development of alternative SBS generators such as ω-sequence, δ-sequence, σ-sequence, and ζ-sequence that generate strings with specific bit distributions to improve accuracy and reduce hardware requirements, using methods like bit grouping and distribution algorithms to minimize transitions and adhere to additive inverse identities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If stochastic binary string (SBS) representations are used for multiplication operations, then multiplication can be performed more efficiently, but large string lengths are required to achieve accurate results, leading to inefficient storage and hardware usage
Solution Approach 1:
The patent transforms the binary representation parameter from deterministic bit positions to probabilistic bit values. Each bit in the stochastic binary string represents a probability value rather than a fixed binary digit, allowing the same numerical value to be represented with shorter strings while maintaining multiplication accuracy through probabilistic computation
2Measurement precision
If larger string lengths are used in SBS representations, then multiplication accuracy improves, but hardware requirements and storage efficiency deteriorate
Solution Approach 1:
The patent replaces traditional mechanical/deterministic binary multiplication hardware with probabilistic stochastic computation. Instead of using complex digital logic circuits for binary multiplication, the system uses probabilistic bit transitions and statistical convergence to achieve multiplication, significantly reducing hardware complexity while maintaining or improving accuracy
3Speed
If traditional binary representation is used, then storage is compact, but multiplication operations become computationally intensive and slower
Solution Approach 1:
The patent employs periodic probabilistic transitions in stochastic binary strings to perform multiplication. By using repeating probabilistic patterns and statistical convergence over multiple bit positions, the system achieves multiplication through natural probabilistic laws rather than sequential computational steps, dramatically increasing speed while reducing computational resource consumption
Data Source
AI summary
A method and apparatus is disclosed for determining a stochastic binary string (SBS) representing a value based on the value represented in binary two's complement. Several different generators are disclosed for generating SBS strings, each being generated to have particular features that are advantageous under various conditions in which the string is to be multiplied with another SBS string. Several such generators can be presented and selected depending upon the particular values to be converted to SBS representation and the functions to be performed on those values.