# Derive the State Table and the State Diagram of the Sequential Circuit

## State Table of Sequential Circuit:

A sequential circuit is an interconnection of flip-flops and gates. The gates by themselves constitute a combinational circuit. But when it included with the flip-flops, the overall circuit classified as a sequential circuit. It consists of a combinational circuit and several clocked flip-flops. In general, any number or type of flip-flops may be included.

As shown in the diagram, the combinational circuit block receives binary signals from external inputs and the outputs of flip-flops. The outputs of the combinational circuit go to external outputs and inputs of flip-flops. The gates in the combinational circuit determine the binary value to be stored in the flip-flops after each clock transition.

The outputs of flip-flops, in turn, are applied to the combinational circuit inputs and determine the circuit’s behaviour. This process demonstrates that the external results of a sequential circuit. Those circuits are functions of both external inputs and the present state of the flip-flops. Moreover, the next state of flip-flops is also a function of their present state and external inputs. Thus a sequential circuit is specified by a time sequence of external inputs, external outputs, and internal flip-flop binary states.

## State Diagram of Sequential Circuit:

The information in a state table can be graphically represented in a state diagram. In this type of diagram, a state represented by a circle, and the transition between states indicated by directed lines connecting the circles. The state diagram of the sequential circuit given below.

The state diagram provides the same information as the state table. The binary number inside each circle identifies the state of the flip-flops. The directed lines labelled with two binary numbers separated by a slash. The input value during the present state labelled first and the number after the slash gives the output during the present state.

For example, the directed line from state 00 to 01 labelled 1/0. It means that when the sequential circuit is in the present state 00 and the input is 1, the output is 0. After a clock transition, the circuit goes to the next state 01. The same clock transition may change the input value. If the input changes to 0, the output becomes 1. But if the input remains at 1, the output stays at 0. This information obtained from the state diagram along the two directed lines from the circle representing state 01. A directed line connecting a circle with itself indicates that no change of state occurs.