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Parallel Unary Computing Based on Function Derivatives

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Published:28 October 2020Publication History
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Abstract

The binary number representation has dominated digital logic for decades due to its compact storage requirements. An alternative representation is the unary number system: We use N bits, from which the first M are 1 and the rest are 0 to represent the value M/N. One-hot representation is a variation of the unary number system where it has one 1 in the N bits, where the 1’s position represents its value. We present a novel method that first converts binary numbers to unary using thermometer (one-hot) encoders and then uses a “scaling network” followed by voting gates that we call “alternator logic,” followed by a decoder to convert the numbers back to the binary format. For monotonically increasing functions, the scaling network is all we need, which essentially uses only the routing resources and flip-flops on a typical FPGA architecture. Our method is clearly superior to the conventional binary implementation: Our area×delay cost is on average only 0.4%, 4%, and 39% of the binary method for 8-, 10-, and 12-bit resolutions, respectively, in thermometer encoding scheme, and 0.5%, 15%, and 147% in the one-hot encoding scheme. In terms of power efficiency, our one-hot method is between about 69× and 114× better compared to conventional binary.

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        • Published in

          cover image ACM Transactions on Reconfigurable Technology and Systems
          ACM Transactions on Reconfigurable Technology and Systems  Volume 14, Issue 1
          March 2021
          138 pages
          ISSN:1936-7406
          EISSN:1936-7414
          DOI:10.1145/3418746
          • Editor:
          • Deming Chen
          Issue’s Table of Contents

          Copyright © 2020 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 28 October 2020
          • Accepted: 1 August 2020
          • Revised: 1 June 2020
          • Received: 1 August 2019
          Published in trets Volume 14, Issue 1

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