Synthesis of UP-DOWN Counters

IN this paper we will describe an algorithm for the decomposition of UP-DOWN counters. The constituents of the decomposed counters will be UP-DOWN counters of small modulus and small amounts of combinatorial logic. The main advantage accruing from this decomposition technique is that only a small number of building blocks is required to build counters with any modulus. We will begin the discussion by developing analysis techniques for particular interconnections of UP-DOWN counters. Following this, a general technique for the synthesis of an UP-DOWN counter with any modulus will be given. Only binary and ternary UP-DOWN counters and a small amount of combinatorial logic will be required.