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Session # 2793 Multimedia

A Systematic Design Procedure for Asynchronous Counters Using El Naga’s Transitions Technique

Nagi M. El Naga, Halima M. El Naga California State University, California State Polytechnic University, Northridge Pomona

Abstract

Although asynchronous counters have been discussed in almost every logical circuits design textbook, they all failed to provide the readers with a systematic design procedure. This is due to the fact that the conventional method of designing sequential circuits lacks the means to provide such procedure. In this paper, a systematic procedure for designing asynchronous counters based on the use of El Naga’s Transitions technique is presented. This technique is based on the use of the four transitions: α, the transition from 0 to 1, β, the transition from 1 to 0, I, the transition from 1 to 1, and ϕ, the transition from 0 to 0. This technique also provides the designer of logical sequential circuits with various testing algorithms that check the correctness of almost every step in the design procedure. If the provided testing algorithms are followed after each step of the design, the final design will be almost error free.

The design techniques presented in this paper make the process of designing asynchronous counters much simpler and, more importantly, make the process of teaching them much easier.

I. Introduction

In this section, the four transitions used in El Naga’s Transitions technique [1] are first presented. Then, the excitation equation of each data input of each type of flip-flop is driven in terms of these four transitions.

During the transition from one state to another, a flip-flop can go through one of four possible transitions, which are defined as:

1. α, the transition from 0 to 1, 2. β, the transition from 1 to 0, 3. I, the transition from 1 to 1, and 4. ϕ, the transition from 0 to 0.

The transition methodology is based on the use of these four transitions. For a particular data input of a specific type of flip-flop, any of the above transitions could be either an

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El Naga, N., & El Naga, H. M. (2001, June), A Systematic Design Procedure For Asynchronous Counters Using El Naga's Transitions Technique Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9839