Читать книгу Digital System Design using FSMs - Peter D. Minns - Страница 35

Produce the Boolean equation for P in state s3 that would satisfy this requirement.

The Boolean equation for P which will produce a 101 sequence when x = 0 is:

P = s3·/x.

Note you do not need to indicate the clk, as it is assumed. Also note that in this case qualifying with NOT x (/x), rather than with x, as in Figure 1.22.

Figure 1.22 State diagram with Mealy P output in s3.

It is very likely that you came up with a different set of values for the secondary state assignments to those obtained. This is fine since there is no real preferred set of assignments, apart from trying to obtain a unit distance coding (ABC values not shown at this stage).

Try re‐drawing the state diagram with the dummy state and modified coding.

Note: care should be taken where you place the dummy state. If you added a dummy state between states s1 and s2, for example, it would alter the P output sequence so that, instead of producing, say, 101, the sequence 1001 would be produced.

A safe place to add a dummy state would be between states s3 and s4, or between states s4 and s0 since they are outside the ‘critical P’ sequence generating in this part of the state diagram.

Turn to Frame 1.21 for the timing waveform diagram solution.