Utilization of Modular Eight-Variable Karnaugh Maps in Digital Design

This chapter introduces a regular and modular version of the 8-variable Karnaugh map, which is a map having an unusually high variable-handling capability. The chapter also analyzes an n-bit comparator in the general case of arbitrary n and visualizes this analysis for n = 4 on the afore-mentioned map. The cases n = 3, 2, and 1 appear as special cases on 6-variable, 4-variable, and 2-variable submaps of the original map. The evaluation is a tutorial exposition of several important ideas in switching theory, such as implicants, prime implicants, essential prime implicants, minimal sum, complete sum, disjoint sum of products (or probability-ready expressions), Boole-Shannon Expansion, and unate and threshold functions.