Some remarks on linear transform of variables in representation of adders by word-level expressions and spectral transform decision diagrams

Abstract

This paper discusses transforms for the reduction of complexity of different representations for binary adders described by binary-valued multiple-output functions and integer-valued single-output functions. For these bit-level and word-level representations of adders, we compared the complexity of the corresponding polynomial expressions and related decision diagrams. We discuss a linear transform of input variables for optimization of AND-OR and AND-EXOR expressions for n-bit adders. The relationships of this transform to the method for linearization of multiple-output switching functions through the total autocorrelation function are shown. Due to that we extend the application of that transform to word-level expressions for adders. We discuss the impact of this transform to the characteristics of different word-level decision diagrams considered as the graphic representations of related word-level expressions.