Fast and low-power leading-one detectors for energy-efficient logarithmic computing

The logarithmic number system (LNS) can be used to simplify the computation of arithmetic functions, such as multiplication. This article proposes three leading-one detectors (LODs) to speed up the binary logarithm calculation in the LNS. The first LOD (LOD I) uses a single fixed value to approximate the d least significant bits (LSBs) in the outputs of the LOD. The second design (LOD II) partitions the d LSBs into smaller fields and uses a multiplexer to select the closest approximation to the exact value. These two LODs help with error cancellation as they introduce signed errors for inputs N < 2^d. Additionally, a scaling scheme is proposed that scales up the input N < 2^d to avoid large approximation errors. Finally, an improved exact LOD (LOD III) is proposed that only passes half of the input N to the LOD; the more significant half is passed if there is at least one ‘1’ in that half; otherwise, the less significant half is passed. Our simulation results show that the 32-bit LOD III can be up to 2.8× more energy-efficient than existing designs in the literature. The Mitchell logarithmic multiplier and a neural network are considered to further illustrate the practicality of the proposed designs.