Approximate Radix-8 Booth Multipliers for Low-Power and High-Performance Operation
Bibliographic record
Abstract
The Booth multiplier has been widely used for high performance signed multiplication by encoding and thereby reducing the number of partial products. A multiplier using the radix-$4$(or modified Booth) algorithm is very efficient due to the ease of partial product generation, whereas the radix-$8$Booth multiplier is slow due to the complexity of generating the odd multiples of the multiplicand. In this paper, this issue is alleviated by the application of approximate designs. An approximate$2$-bit adder is deliberately designed for calculating the sum of$1\times$and$2\times$of a binary number. This adder requires a small area, a low power and a short critical path delay. Subsequently, the$2$-bit adder is employed to implement the less significant section of a recoding adder for generating the triple multiplicand with no carry propagation. In the pursuit of a trade-off between accuracy and power consumption, two signed$16\times 16$bit approximate radix-8 Booth multipliers are designed using the approximate recoding adder with and without the truncation of a number of less significant bits in the partial products. The proposed approximate multipliers are faster and more power efficient than the accurate Booth multiplier. The multiplier with 15-bit truncation achieves the best overall performance in terms of hardware and accuracy when compared to other approximate Booth multiplier designs. Finally, the approximate multipliers are applied to the design of a low-pass FIR filter and they show better performance than other approximate Booth multipliers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".