A Novel Cotransformation for LNS Subtraction

Abstract

The Logarithmic Number System (LNS) can be considered a simplification of the Floating Point (FP) Number System that assumes the mantissa is always equal to one, and has a binary fixed-point exponent. LNS converts multiplication/division to a single addition/subtraction, which make LNS a very attractive choice for applications where these operations predominate, such as in some signal-processing algorithms. However, for wordlengths greater than 20 bits LNS becomes expensive because of the hardware-demanding LNS operations of addition and subtraction, which are typically important for most signal-processing algorithms. This paper gives an overview of the family of LNS subtraction algorithms called "Cotransformations," and proposes a "Novel Cotransformation Combination" that offers improvements in terms of area and speed without sacrificing accuracy compared to previous methods. The hardware requirements of the proposed method are analyzed mathematically, and the results are verified by using synthesis and simulations.