Analysis of Clocked Sequential Circuits

Example of a Sequential Circuit

D flip-flops

Example: Start with A=0, B=0, x=0.A(next)=0B(next)=0Y(next)=0

What are A(next), B(next) and y(next) given that A=1, B=1 and X=1?

D flip-flops

Alternate State Table

State Diagram

Each circle is a state

When x=1, y=0.

State Diagram

Each circle is a state

When x=0, y=1.

Detects 0 in the bit stream of data

Output is a 0 as long as input is a 1. The first 0 after a string of 1 transfers the circuit back to 00.

Summary

Model a Clocked Sequential Circuit with Verilog

1. Use parameter to define constants2. Form the next state from x and the current state3. Form the output4. fork.....join construction

S0

S1

S2

S3

Parameter

S0

S1

S2

S3

Define states with parameter

Update States

S0

S1

S2

S3

If reset is 0, set state to S0.

If reset is 1, update state with next_state.

Implement the States Using State Diagram

S0

S1

S2

S3

fork....join

Right click to add state and next_state to the waveform shown right

Valid Mealy Output

S0

S1

S2

S3

Mealy Glitches

S0

S1

S2

S3

Glitiches occur because x changes before the next rising clock edge

General Structure of a Mealy Machine

Output depends on input as well as the stateThe circuit is in. (variable: state)

Synchronize the input with clock when using Mealy machine.

Moore Machine

Output depends on the state, but not the input.

Synthesis of Sequential Circuit

• Start with a state diagram• Assign Binary Values to the States

State Diagram for Sequence Detector

• Problem statement:–Design a circuit that detects a

sequence of three or more consecutive 1’s in a string of bits coming through an input line

State Diagram of the Word Description

Start with S0.if input is 0, stay in S0.if input is 1, go to S1.

Once in S1if input is 1, go to S2.if input is 0, go to S0.

Once in S2if input is 0, go to S0.if input is 1, go to S3.

Once in S3,if input is 0, go to S0.if input is 1, stay in S3, set output to 1.

Output is 1 when the circuit is in S3, 0 otherwise.

Assign Binary Value to the States

Use two flip-flops to represent states.Let x be the inputAnd y be the output

01234567

Assign Binary Value to the States

01234567

Circuit Implementation

Sequence Detector Circuit

Random Numbergenerator

SequenceDetector

Measurement Results

A

B

x

y

clk