State assignment for hardwired VLSI control units

Abstract

Finding a binary encoding of symbolic control states, such that the implementation area of a digital control unit is minimized is well known to be NP-complete. Many heuristic algorithms have been proposed for this state assignment problem . The objective of this article is to present a comprehensive survey and systematic categorization of the various techniques, in particular, for synchronous sequential circuits with nonmicroprogrammed implementations. The problem is partitioned into the generation and the satisfaction of coding constraints. Three types of coding constraints—adjacency, covering, and disjunctive constraints—are widely used. The constraint satisfaction algorithms are classified into column-based, row-based, tree-based, dichotomy-based, and global minimization approaches. All of them are illustrated with examples. Special coding requirements and testability-related aspects of state assignment are considered in a separate section. Different implementations of the algorithms presented are also compared.