Approximate Radix-8 Booth Multipliers for Low-Power and High-Performance Operation
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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- <inline-formula><tex-math notation="LaTeX">$4$ </tex-math></inline-formula> (or modified Booth) algorithm is very efficient due to the ease of partial product generation, whereas the radix- <inline-formula><tex-math notation="LaTeX">$8$</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">$2$</tex-math> </inline-formula> -bit adder is deliberately designed for calculating the sum of <inline-formula><tex-math notation="LaTeX">$1\times$</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$2\times$</tex-math></inline-formula> of a binary number. This adder requires a small area, a low power and a short critical path delay. Subsequently, the <inline-formula><tex-math notation="LaTeX">$2$</tex-math></inline-formula> -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 <inline-formula> <tex-math notation="LaTeX">$16\times 16$</tex-math></inline-formula> 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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it