TRANSITION LOGIC CIRCUITS AND A SYNTHESIS METHOD

A transition signal is a change of binary level, either from 0 to 1 or from 1 to 0, regardless of the direction. It is often more convenient to describe a switching circuit in terms of level transitions, and a circuit with at least one input variable represented as a transition signal is called a transition logic circuit. Transition logic circuits are essentially level sequential circuits and, as such, Huffman's synthesis method can be applied. However, Huffman's synthesis rapidly becomes too laborious as the number of transition variables increases. The first part of this paper presents a synthesis approach which is simpler than Huffman's in such cases, although its applicability is more limited. In this approach, one considers a level transition as if it were a pulse, and then synthesizes the circuit following the standard pulse sequential circuit synthesis method. Circuits are constructed from two basic transition logic elements, the G element and the M element, together with ordinary gates. The second part of the paper presents a new economical state assignment method. The assignment results in a realization with fewest G elements as well as fewest level functions formed by the associated level combinational circuit. This assignment method is also applicable to the seldom discussed problem of state assignment in the synthesis of pulse sequential circuits using complementary flip-flops as memory elements. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.