Preprint Open Access

On the optimality of ternary arithmetic for compactness and hardware design

Harris Georgiou

Abstract

In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as the main parameter to assess the efficiency of the representation, in terms of information compactness and estimated implementation cost in hardware. Using proper formulations for the optimization task, the universal constant e (base of natural logarithms) is proven as the most efficient radix and ternary is asserted as the closest integer choice.

Name Size
binary-ternary-arithmetic.pdf
md5:a2053fa2befe2d0b8aff28e6bbe0b2db
377.4 kB Download

Share

Cite as