One-Hot Residue Logarithmic Number Systems

Abstract

Switching behavior and dynamic power consumption of arithmetic circuits are influenced by the distribution of operands as well as the number system used to encode them. Binary integer encoding may cause severe switching fluctuation; the integer Residue Number System (RNS) reduces this by breaking the integer into smaller moduli, which in turn may use either binary or one-hot encoding. One-hot switching is nearly consistent regardless of operand distribution, but this comes at the cost of increased bit width. Reals are represented by mapping integers, such as well-known examples of fixed point and Floating Point (FP). A more unusual system is the Logarithmic Number System (LNS) that takes the logarithm of the absolute value of the real (its sign is encoded separately) into an integer. Combining one-hot, RNS and LNS offers real arithmetic circuits with nearly uniform switching at the cost of some complexity in word size, addition, conversion and sign-detection.