Efficient Realization of BCD Multipliers Using FPGAs
Bibliographic record
Abstract
In this paper, a novel BCD multiplier approach is proposed. The main highlight of the proposed architecture is the generation of the partial products and parallel binary operations based on 2-digit columns. 1 × 1-digit multipliers used for the partial product generation are implemented directly by 4-bit binary multipliers without any code conversion. The binary results of the 1 × 1-digit multiplications are organized according to their two-digit positions to generate the 2-digit column-based partial products. A binary-decimal compressor structure is developed and used for partial product reduction. These reduced partial products are added in optimized 6-LUT BCD adders. The parallel binary operations and the improved BCD addition result in improved performance and reduced resource usage. The proposed approach was implemented on Xilinx Virtex-5 and Virtex-6 FPGAs with emphasis on the critical path delay reduction. Pipelined BCD multipliers were implemented for 4 × 4, 8 × 8, and 16 × 16-digit multipliers. Our realizations achieve an increase in speed by up to 22% and a reduction of LUT count by up to 14% over previously reported results.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 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".