Analysis With T Flip-Flops

ANALYSIS WITH T FLIP-FLOPS

As with JK flip-flops, the next state values can be obtained either by using the characteristic table:

or by the characteristic equation:

Consider the following sequential circuit:

It can be described algebraically by two input equations and an output equation:

TA = BX   TB = X       y = AB

The state table for this circuit is listed below:

The values for y are obtained from the output equation. The values for the next state can be derived from the state equations by substituting TA and TB in the characteristic equations, yielding:

A(t+1) = (BX)’A + (BX)A’ = AB’ + AX’ + A’BX

The state diagram for the circuit is shown below:

As long as input x is equal to 1, the circuit behaves as a binary counter with a sequence of states 00, 01, 10, 11, and back to 00.

When x = 0, the circuit remains in the same state. Output y is equal to 1 when the present state is 11. The output depends on the present state only and is independent of the input.

The two values inside each circle separated by a slash are for the present state and output.