Design and Analysis of Area and Power Efficient Approximate Booth Multipliers
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Bibliographic record
Abstract
Approximate computing is an emerging technique in which power-efficient circuits are designed with reduced complexity in exchange for some loss in accuracy. Such circuits are suitable for applications in which high accuracy is not a strict requirement. Radix-4 modified Booth encoding is a popular multiplication algorithm which reduces the size of the partial product array by half. In this paper, three Approximate Booth Multiplier Models (ABM-M1, ABM-M2, and ABM-M3) are proposed in which approximate computing is applied to the radix-4 modified Booth algorithm. Each of the three designs features a unique approximation technique that involves both reducing the logic complexity of the Booth partial product generator and modifying the method of partial product accumulation. The proposed approximate multipliers are demonstrated to have better performance than existing approximate Booth multipliers in terms of accuracy and power. Compared to the exact Booth multiplier, ABM-M1 achieves up to a 23 percent reduction in area and 15 percent reduction in power with a Mean Relative Error Distance (MRED) value of 7:9 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . ABM-M2 has area and power savings of up to 51 and 46 percent respectively with a MRED of 2:7 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . ABM-M3 has area savings of up to 56 percent and power savings of up to 46 percent with a MRED of 3:4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The proposed designs are compared with the state-of-the-art existing multipliers and are found to outperform them in terms of area and power savings while maintaining high accuracy. The performance of the proposed designs are demonstrated using image transformation, matrix multiplication, and Finite Impulse Response (FIR) filtering applications.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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)
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 it