A novel decimal-to-decimal logarithmic converter
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Bibliographic record
Abstract
This paper presents a novel design and implementation of a 7-digit fixed-point decimal-to-decimal logarithmic converter. Two approaches, binary-based decimal approximation algorithm (Algorithm 1) and decimal linear approximation algorithm (Algorithm 2), are proposed and investigated. It shows that decimal linear approximation algorithm (Algorithm 2) is error-free in conversion between decimal and binary formats and also able to reduce maximum absolute error from binary-based Algorithm 1’s 0.00399 (integer cases) and 0.0483 (fraction cases) to 0.000994 (both cases). The Algorithm 2 is modeled in VHDL and implemented using combinational logic only in a Xilinx Virtex-II Pro P30 FPGA device. The logarithms results can be obtained in a single clock cycle, running at 50.9 MHz.
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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 | 0.001 |
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 it