Design of Approximate Radix-4 Booth Multipliers for Error-Tolerant Computing
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Bibliographic record
Abstract
Approximate computing is an attractive design methodology to achieve low power, high performance (low delay) and reduced circuit complexity by relaxing the requirement of accuracy. In this paper, approximate Booth multipliers are designed based on approximate radix-4 modified Booth encoding (MBE) algorithms and a regular partial product array that employs an approximate Wallace tree. Two approximate Booth encoders are proposed and analyzed for error-tolerant computing. The error characteristics are analyzed with respect to the so-called approximation factor that is related to the inexact bit width of the Booth multipliers. Simulation results at 45 nm feature size in CMOS for delay, area and power consumption are also provided. The results show that the proposed 16-bit approximate radix-4 Booth multipliers with approximate factors of 12 and 14 are more accurate than existing approximate Booth multipliers with moderate power consumption. The proposed R4ABM2 multiplier with an approximation factor of 14 is the most efficient design when considering both power-delay product and the error metric NMED. Case studies for image processing show the validity of the proposed approximate radix-4 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 | 0.000 |
| Open science | 0.001 | 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