Parallel Unary Computing Based on Function Derivatives

Soheil Mohajer

doi:10.1145/3418464

Parallel Unary Computing Based on Function Derivatives

2020-10-28

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DOI：10.1145/3418464

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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 areaxdelay 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 69x and 114x better compared to conventional binary.

Keywords:

Unary computing

scaling network

alternator logic

stochastic computing

thermometer code

Parallel Unary Computing Based on Function Derivatives

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