Sequential-circuit characterisation and synthesis using a `transition-equation¿ approach

The characteristics of combinational and sequential circuits or networks can be expressed in `transition-equation¿ form. Transition characteristic equations carry complete information on the behaviour of the circuit, and are readily derived for any circuit or from any reasonable circuit data sheet. Synchronous, clock and asynchronous inputs can be shown, and also the nature of the clock activation, where appropriate. Propagation delays may also be manipulated with the characteristic expressions. Network characteristics can also be expressed in terms of desired transitions from one state to another, and this leads to straightforward synthesis procedures when circuit characteristics are in transition-equation form. Analysis is equally straightforward. The paper briefly introduces transition characteristic equations by way of J-K flip-flops and NAND gates, and then uses a simple example to illustrate the approach to synthesis. It is clearly shown that the transition equations allow for several different approaches to be taken to the same problem. Hazards due to propagation delays are also revealed, which is particularly helpful, for example, when dealing with `ripple-through¿ arrays.