Area-Time Optimal Fast Implementation of Several Functions in a VLSI Model

Abstract

Area and computation time are considered to be important measures with which VLSI circuits are evaluated. In this paper, the area-time complexity for nontrivial n-input m-output Boolean functions, such as a decoder and an encoder, is studied with a model similar to Brent-Kung's model. A lower bound on area-time-product (ATαaα.≥1) for these functions is shown: for example, AT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> = ω(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α-l</sup> ) for an n-input 2V-output decoder, and AT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> = ω( n . log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α-1</sup> n) for an n-input ⌈log n⌉-output encoder. The results shown in this paper are complementary to those by Brent-Kung or Thompson, and are useful for a class of functions of rather simple structures, e.g., a priority encoder, a comparator, and symmetric functions.