# T flip-flop

## Introduction

T flip-flop is the simplified version of JK flip-flop. It is obtained by connecting the same input ‘T’ to both inputs of JK flip-flop. It operates with only positive clock transitions or negative clock transitions. The circuit diagram of T flip-flop is shown in the following figure.

This circuit has single input T and two outputs Q(t) & Q(t)’. The operation of T flip-flop is same as that of JK flip-flop. Here, the inputs of JK flip-flop are considered as J = T and K = T in order to utilize the modified JK flip-flop for 2 combinations of inputs. So, the other two combinations of J & K are eliminated, for which those two values are complement to each other in T flip-flop.

## State table

D Q(t+1)
0 Q(t)
1 Q(t)’

Here, Q(t) & Q(t + 1) are present state & next state respectively. So, T flip-flop can be used for one of these two functions such as Hold, & Complement of present state based on the input conditions, when positive transition of clock signal is applied.

## Characteristic table

T Q(t) Q(t + 1)
0 0 0
0 1 1
1 0 1
1 1 0

From the above characteristic table, the next state equation can be directly written as:

``````          Q(t + 1) = T'.Q(t) + T.Q(t)'
=> Q(t + 1) = T ⊕ Q(t)
``````

The output of T flip-flop always toggles for every positive transition of the clock signal, when input T remains at logic High (1). Hence, T flip-flop can be used in counters.