Parallel Unary Computing Based on Function Derivatives

Soheil Mohajer, Zhiheng Wang, Kia Bazargan, Yuyang Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Article number4
JournalACM Transactions on Reconfigurable Technology and Systems
Issue number1
StatePublished - Dec 2020

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation, under grant number 1408123 (CCF-SHF). Authors’ addresses: S. Mohajer, Z. Wang, K. Bazargan, and Y. Li, Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455; emails: {soheil, wang3868, kia, li001130} Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from © 2020 Association for Computing Machinery. 1936-7406/2020/10-ART4 $15.00

Publisher Copyright:
© 2020 ACM.


  • Unary computing
  • alternator logic
  • scaling network
  • stochastic computing
  • thermometer code


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