Logarithmic number systems (LNS) are used to represent real numbers in many applications using a constant base raised fixed-point exponent making its distribution exponential. This greatly simplifies hardware multiply, divide, and square root. LNS with base-2 is most common, but this article, we show that for low-precision the choice of has significant impact. We make four main contributions. F...

signed digit (sd) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. such carry-free addition is primarily a three-step process; adding the equally weighted sds to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the transfers to...