Introduction to Sequential Circuit By : Pn Siti Nor Diana Ismail CHAPTER 5.
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Transcript of Introduction to Sequential Circuit By : Pn Siti Nor Diana Ismail CHAPTER 5.
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