T Flip-Flop

The T flip-flop is a single input version of the JK flip-flop. As shown in Figure 7, the T flip-flop is obtained from the JK type if both inputs are tied together. The output of the T flip-flop "toggles" with each clock pulse.
The state of a flip-flop is changed by a momentary change in the input signal. This change is called a trigger and the transition it causes is said to trigger the flip-flop. The basic circuits of Figure 2 and Figure 3 require an input trigger defined by a change in signal level. This level must be returned to its initial level before a second trigger is applied. Clocked flip-flops are triggered by pulses.
The feedback path between the combinational circuit and memory elements in Figure 1 can produce instability if the outputs of the memory elements (flip-flops) are changing while the outputs of the combinational circuit that go to the flip-flop inputs are being sampled by the clock pulse. A way to solve the feedback timing problem is to make the flip-flop sensitive to the pulse transition rather than the pulse duration. The clock pulse goes through two signal transitions: from 0 to 1
and the return from 1 to 0. As shown in Figure 8 the positive transition is defined as the positive edge and the negative transition as the negative edge.

The clocked flip-flops already introduced are triggered during the positive edge of the pulse, and the state transition starts as soon as the pulse reaches the logic-1 level. If the other inputs change while the clock is still 1, a new output state may occur. If the flip-flop is made to respond to the positive (or negative) edge transition only, instead of the entire pulse duration, then the multiple-transition problem can be eliminated.
Summary
Since memory elements in sequential circuits are usually flip-flops, it is worth summarising the behaviour of various flip-flop types before proceeding further. All flip-flops can be divided into four basic types: SR, JK, D and T. They differ in the number of inputs and in the response invoked by different value of input signals. The four types of flip-flops are defined in Table 1.
Table 1. Flip-flop Types