Multiplier Circuit With Carry-Based Radix-4 Encoding for Lower Area and Power
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Solution Overview
Problem
Existing multiplier circuits in integrated circuits, particularly in AI and high-performance computing, are area and power inefficient due to conventional Booth's encoding schemes, which do not effectively reduce the complexity of partial product generation.
Innovation Solution
Implementing a carry-based radix 4 encoding scheme that reduces the number of possible codings by depending on previous encoders, using a carry-based radix 4 multiplier encoder with fewer gates and a partial product multiplexer, thereby reducing die area and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional Booth's encoding schemes are used in multiplier circuits, then the multiplier can perform multiplication operations, but the device area and power consumption increase due to higher complexity in partial product generation
Solution Approach 1:
The patent changes the encoding parameters by transitioning from conventional Booth's encoding to a carry-based radix 4 encoding scheme. This parameter change reduces the number of possible codings from 5 to 4, which directly simplifies the partial product generation complexity and reduces the number of gates required in the multiplier circuit, thereby reducing die area.
Solution Approach 2:
The patent extracts and removes one of the five possible multiplication codes from Booth's encoding scheme by incorporating carry dependency. This extraction reduces the coding space from 5 codes to 4 codes, simplifying the encoder logic and reducing the complexity of the partial product generation circuitry, which directly reduces the required die area.
2Device complexity
If conventional Booth's encoding schemes are used in multiplier circuits, then the multiplier can perform multiplication operations, but power consumption increases due to higher complexity in partial product generation
Solution Approach 1:
The patent changes the encoding parameters by transitioning from conventional Booth's encoding to a carry-based radix 4 encoding scheme. This parameter change reduces the number of possible codings from 5 to 4, which directly simplifies the partial product generation complexity and reduces the number of gates required in the multiplier circuit, thereby reducing power consumption.
Solution Approach 2:
The patent extracts and removes one of the five possible multiplication codes from Booth's encoding scheme by incorporating carry dependency. This extraction reduces the coding space from 5 codes to 4 codes, simplifying the encoder logic and reducing the complexity of the partial product generation circuitry, which directly reduces power consumption.
3Area of stationary object
If a carry-based radix 4 encoding scheme is implemented, then the number of possible codings is reduced and die area is minimized, but the encoding depends on previous encoders requiring carry signal propagation
Solution Approach 1:
The patent introduces carry signal propagation as a feedback mechanism where the carry output of one encoder stage is fed back as the carry input to the next encoder stage. This feedback mechanism manages the dependency chain between encoders, allowing the carry-based radix 4 encoding to proceed systematically through all bit pairs while maintaining the reduced coding space benefit.
Data Source
AI summary
Integrated circuit devices, methods, and circuitry for an efficient multiplier are provided. Multiplier circuitry to multiply a multiplicand value with a multiplier value may include, among other things, input circuitry and carry-based coding circuitry. The input circuitry may receive the multiplicand value and the multiplier value. The carry-based coding circuitry may receive bits of the multiplier value and generate multiplication codes using a carry-based coding scheme that includes multiplication codes according to a Booth's coding scheme but with at least one multiplication code that is removed and replaced with another at least one multiplication code with a different value. A first encoder of the carry-based coding circuitry may receive a carry signal to adjust a multiplication code value of the first encoder based on a second encoder of the carry-based coding circuitry encoding the multiplication code with the different value.