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.