Majority Logic-based Approximate Recoding Adders for High-radix Booth Multipliers
Bibliographic record
Abstract
Approximate computing permits the improvement of hardware efficiency with a relaxation of accuracy for nanoscale technologies and devices. Instead of conventional Boolean logic, voter-based majority logic (ML) is widely applicable to many emerging nanotechnologies. High-radix Booth multipliers, such as radix-8 and radix-16 multipliers, suffer from high complexity when generating odd multiples of the multiplicand. In this paper, designs of approximate recording adders (ARAs) based on ML with no carry propagation are proposed to alleviate this issue. For calculating the triple and 5×of the multiplicand, a 2-bit ARA and a 3-bit ARA are designed to compute the sum of 1× and 2× multiplicand, and the sum of 1× and 4× multiplicand, respectively. Moreover, a 4-bit ARA is especially developed for computing 7× of the multiplicand as the addition of −1× and 8× of the multiplicand. The proposed ARAs show advantages in hardware evaluated by delay and gate complexity, as well as in accuracy; for example, in a 16 × 16 radix-8 multiplier, the use of 2-bit ARAs achieves a reduction of 77% in the area-delay product with a normalized mean error distance of 7.51 × 10–4for computing the triple multiplicand.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".