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

**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.

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Digital Electronics : Synchronous and Asynchronous Sequential Circuits : Analysis With T Flip-Flops |

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