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# Conversion of JK Flip-Flop into T Flip-Flop

## What is a JK Flip-Flop?

JK flip flop is also a 1-bit storage device having two inputs similar to SR flip flop, but it has inputs denoted by J and K instead of S and R. It has two outputs viz. Q (normal output) and Q' (inverted output). The clock signal is used for synchronization of the circuit.

The block diagram of the JK flip flop is shown in Figure-1 below.

The operation of the JK flip flop can be understood with the help of its truth table which is given below −

Inputs | Output | |
---|---|---|

J | K | Q_{n+1} |

0 | 0 | Qn |

0 | 1 | 0 |

1 | 0 | 1 |

1 | 1 | Toggle |

The characteristic equation of the JK flip flop is given by,

$$Q_{n+1}=JQ_{n}^{'}+K'Q_{n}$$

## What is a T Flip-Flop?

**T flip-flop**, also called **toggle flip flop**, is a type of digital flip flop which has a single input
specified by the letter T. It has two outputs namely Q and Q', where Q is the normal output
and Q' is the complemented output.

The block diagram of T flip flop is shown in Figure-2.

The truth table of the T flip flop is depicted below.

Input (T) | Present State of Output
(Q |
Next State of Output
(Q |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

From the truth table of the T flip flop, it is clear that when the input T is equal to 0, there is no change in the output of the flip flop. When T is equal to 1, the output of the T flip flop toggles.

The characteristics equation of the T flip flop is given by,

$$Q_{n+1}=T'Q_{n}+TQ_{n}^{'}$$

After discussing the basics of JK flip flop and T flip flop, let us now discuss the conversion of JK flip flop into T flip flop.

## Conversion of Flip-Flop

We can convert a one type of flip-flop into another type of flip-flop. The conversion process of flip-flops involves the following steps −

**Step 1**− Write the excitation table of the flip flops.**Step 2**− Simplify the excitation table with the help of Karnaugh Map (K-map).**Step 3**− Draw the required logic circuit diagram.

Now, let us convert the JK flip-flop into the T flip-flop.

## Conversion of JK Flip-Flop into T Flip-Flop

The conversion of JK flip-flop into T flip-flop is done as per the following steps −

**Step 1** − The excitation table for the conversion of JK flip flop to T flip flop is given below.

Input | Present State of Output | Next State of Output | Flip Flop Inputs | |||
---|---|---|---|---|---|---|

T | Q_{n} | Q_{n+1} | J | K | J | K |

0 | 0 | 0 | 0 | 0 | 0 | X |

0 | 1 | |||||

0 | 1 | 1 | 0 | 0 | X | 0 |

1 | 0 | |||||

1 | 0 | 1 | 1 | 0 | 1 | X |

1 | 1 | |||||

1 | 1 | 0 | 0 | 1 | X | 1 |

1 | 1 |

**Step 2** − The excitation table is simplified by using K-Map technique to obtain the expression
of inputs as follows −

The K-map simplification for the input J is,

**J = T**

The K-map simplification for the input K is,

**K = T**

**Step 3** − The logic diagram of the T flip-flop using JK flip flop is shown in Figure-3 below.

In this way, we can convert JK flip flop into T flip flop.