Alignment Shifter for Booth Encoding Partial Product Reduction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing hardware implementations of binary multiplication in computing systems face challenges in efficiently handling large binary numbers, particularly in reducing the number of partial products and optimizing hardware components for operations like 64 by 64 bit multiplication, where Booth Encoding helps but still requires complex carry save adder structures.
Innovation Solution
A method and system that utilize a carry-save adder, multiplexer, and alignment shifter to efficiently combine partial products, where the alignment shifter adds an extra partial product to the results of binary multiplication, reducing the number of hardware components needed and optimizing power consumption by using existing hardware for both integer and floating-point operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If Booth encoding is used to reduce the number of partial products in 64x64 bit multiplication, then the number of partial products is reduced to 33, but an additional 3rd term must be handled requiring complex carry save adder structures
Solution Approach 1:
The alignment shifter is designed to perform multiple functions: it shifts the 3rd term in integer multiplication operations and aligns the C term in floating-point multiply-add operations. This multi-functionality allows the same hardware to handle both integer and floating-point operations without requiring separate dedicated hardware for each operation type.
Solution Approach 2:
The system dynamically selects between different operation modes (integer multiplication vs. floating-point multiply-add) based on the input type. The alignment shifter adapts its behavior accordingly, shifting the 3rd term for integer operations and aligning the C term for floating-point operations, enabling flexible handling of different computational requirements.
2Reliability
If dedicated hardware components are added to handle the 33rd term in Booth encoding, then complete 64x64 bit integer multiplication is achieved, but hardware component count and power consumption increase
Solution Approach 1:
The alignment shifter serves dual purposes: handling the 3rd term in integer multiplication and aligning the C term in floating-point operations. This eliminates the need for separate dedicated hardware to handle the 33rd term, reducing overall hardware component count and power consumption while maintaining complete integer multiplication capability.
Solution Approach 2:
The functionality for handling the 3rd term in integer multiplication is merged with the existing alignment shifter used for floating-point operations. By combining these functions into a single hardware component, the system reduces the total number of hardware components and decreases power consumption compared to having separate dedicated hardware for each function.
3Adaptability or versatility
If separate hardware is provided for integer and floating-point operations, then each operation type is optimized, but device complexity and resource utilization increase
Solution Approach 1:
The alignment shifter is designed as a universal component that handles both integer multiplication (shifting the 3rd term) and floating-point multiply-add operations (aligning the C term). This multi-functionality allows a single hardware structure to support multiple operation types, reducing device complexity while maintaining adaptability.
Solution Approach 2:
The system dynamically adapts the alignment shifter's behavior based on the operation type being performed. For integer multiplication, it shifts the 3rd term; for floating-point operations, it aligns the C term. This dynamic adaptability enables a single hardware structure to efficiently handle different operation types without requiring separate dedicated hardware for each.
Data Source
AI summary
A computer system for computing a binary operation involving a first term multiplied by a second term resulting in a product, where the product is conditionally added to a third term in a central processing unit. The central processing unit includes a carry save adder configured to add a plurality of partial products obtained from the product of the first term and the second term to obtain a first partial result and a second partial result, a multiplexer configured to output one selected from the group consisting of the second term, the third term, and zero, and an alignment shifter configured to shift an output of the multiplexer to align the output of the multiplexer with the first partial result and the second partial result to obtain a shifted term. The shifted term, the first partial result and the second partial result are added together to obtain a result of the binary operation.