Introduction to Sequential Circuit

By : Pn Siti Nor Diana Ismail

CHAPTER 5

What is Sequential Circuit?

Its behaviour is from :InputsOutputsPresent state

Includes flip-flops with clock inputs

Logic diagram may or may not include combinational gates.

Sequential Circuit Diagram

Important element in sequential circuit :

i. Input equationsii.State tableiii.State diagram

Diagram (A)

Diagram (B)

From previous diagrams (A and B)

You should be able to identify, which part is :The inputsThe outputsThe combinational circuitsThe flip-flop

i. Input Equation

Algebraic expression specifying logic diagram of a sequential circuit

Imply the type of FF used

Fully specify the combinational circuit that drives the

Try to analyze this circuit

What are the elements that you can identify?

Type of flip-flop;Input;Output;The equations of the circuit.

INPUT

EquationsDA =

DB =Y =

STATES

The element are:- Type FFs : D FFs- Input : X, State:A,B- Output : Y- Equation : 3 equations, DA , DB and Y

ii. State Table

Shows functional relationship between inputs, outputs and FF states.

State table consists of:- Present state- Input- Next state- Output

Example : State table

How many rows in state table?

FF = mInputs = n

Number of rows = 2m+n

How to fill in the state table?

STEP 1 : List all possible binary combinations of present state and inputs.

STEP 2 : Next state column is determined by logic diagram or input equations of FF (get the value for all FF inputs and then refer to FF truth table to get the next state value).

STEP 3 : Output column is determined by logic diagram or input equations.

STEP 1List down all binary numbers from 0 to (2m+n – 1) in present state and input column.

Let’s say you have 3 FF and 1 input, number of rows = 23+1 = 16

Binary numbers involved is 0 – 15

STEP 2Determine the next column

Substitute the values in every rows into the FF input equations that you have got earlier.

You will get the input for each FF

Trace down the value for the FF output

STEP 3Determine the output

Substitute the values in every rows into the input equations of output that you have got earlier.

You will directly get the output value

Try to fill in this state table based on the given diagram

So, here is the answer

Types of sequential circuits

Mealy model- Output depend on INPUTS and STATES

Moore model - Output depend on STATES

Circuit Analysis :What type of this circuit?

Circuit Analyze

Just take a look at the output equation

Since Y involves both (A & B) states and (X) input, therefore it is a Mealy model.

XBXAY

Can you differentiate between the previous equation and this one?

The output is Z. Only involves A (state).. So it is a Moore model

AZ

YXADA

iii. State Diagram

State – represented by a circle

Transition between states – directed lines connecting the circles

Examples of State Diagram

Referring to State Diagram (a)

Circuit diagram

State Table

Moore Model

Circuit Diagram

Equation

State Table

AZ

YXADA

State Diagram (Mealy)

Provide same info with state tableObtained from state table

State (A B)

Input (X)

Output (Y)

State Diagram (Moore)

Input X Input Y

State Output

State Table

Exercise 1

A sequential circuit with two D flip-flops A and B, X input , and one output Y is specified by the following input equations :

DA = XA

DB = A+XB’

Y = XBDraw the logic diagram of the circuitDerive the state tableState Diagram

Exercise 2

A sequential circuit with two D flip-flops A and B, two inputs X and Y, and one output Z is specified by the following input equations :

DA = XA + XY

DB = XA + XB

Z = XBDraw the logic diagram of the circuitDerive the state table