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Synchronous Sequential Circuits, Lecture notes of Engineering

The difference between combinational and sequential circuits, and how synchronous sequential circuits employ storage elements in addition to logic gates. It also covers the state table and state diagram representation of sequential circuits, and the difference between Moore and Mealy type circuits. examples of sequence detectors and a clocked sequential circuit design.

Typology: Lecture notes

2021/2022

Available from 12/22/2022

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Synchronous Sequential Circuits 1
DIGITAL CIRCUITS
Logic circuits for digital systems may be
combinational or sequential.
A combinational circuit consists of logic gates
whose outputs at any time are determined
from the present combination of inputs.
A combinational circuit performs an operation
that can be specified logically by a set of Boolean
functions.
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Synchronous Sequential Circuits

DIGITAL CIRCUITS

Logic circuits for digital systems may be combinational or sequential.

A combinational circuit consists of logic gates whose outputs at any time are determinedfrom the present combination of inputs.

A combinational circuit performs an operation that can be specified logically by a set of Booleanfunctions.

Synchronous Sequential Circuits

DIGITAL CIRCUITS

Synchronous Sequential Circuits

employ storage

elements in addition to logic gates.

The outputs of a sequential circuit depend not onlyon present values of inputs, but also on previousinputs.

They are realized using combinational logic and oneor more flip-flops.

Asynchronous Sequential Circuits

  • No clock signal is

used.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

The circuit has a set of primary inputs (W), andproduces a set of outputs (Z).

Under the control of the clock signal, the flip-flopschange their state as determined by thecombinational logic that feeds the inputs of theseflip-flops.

Therefore the circuit moves from one state toanother.

To ensure that only one transition from one state toanother takes place during one clock cycle, the flip-flops have to be edge-triggered.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

The combinational logic that provides theinput signals to the flip-flops derives its inputsfrom two sources:

The primary inputs (W)

The present (current) outputs of the flip-flops (Q)

Therefore changes in state depend on boththe PS and the values of the primary inputs.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

Moore type

: The sequential circuits whose

outputs depend only on the state

of the

circuit.

Mealy type

: The sequential circuits whose

outputs depend only on both the state and the primary inputs

The sequential circuits are also called finitestate machines (FSM). The name drives fromthe fact that the functional behavior of thesecircuits can be represented using a finitenumber of states.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

The first step in designing a finite state machine is todetermine how many states are needed and whichtransitions are possible from one state to another.

A

State Diagram

gives a pictorial representation.

Although the state diagram provides a description ofthe behavior of a sequential circuit that is easy tounderstand, to proceed with the implementation ofthe circuit, it is convenient to translate theinformation contained in the state diagram into atabular form (

State Table

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

A

state machine

is a synchronous

sequential circuit, consisting of a sequentiallogic section and a combinational logicsection, whose outputs and internal flip-flopsprogress through a predictable sequence ofstates in response to a clock and other inputsignals.

The synchronous counters and shift registersare examples of state machines.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

In the synchronous sequential model, the effect of allprevious inputs on the outputs is represented by astate

of the circuit.

The output of the circuit at any time depends uponits current state and the input.

These also determine the next state (NS) of thecircuit.

The relationship that exists among its inputs,outputs, present states (PS) and NS can be specifiedby either the state table or the state diagram.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

The design of a synchronous sequentialcircuit starts from a set of specifications andends in a logic diagram.

From a word description of the problem, form a state table

(or

state diagram

Check this table to determine whether it containsany

redundant states

Select a state assignment, and determine the typeof memory elements to be used.

Synchronous Sequential Circuits

SYNCHRONOUS SEQUENTIAL CIRCUITS

Derive

transition

and

output tables

Derive an

excitation table

and obtain the

excitation and output functions

from their

respective tables.

Draw the circuit diagram.

Synchronous Sequential Circuits

Flip-Flop Excitation Tables

Synchronous Sequential Circuits

Example 1 – Sequence Detector

Design a one-input, one-outputsequence detector which produces anoutput 1 every time the sequence

0101

is detected, and an output 0 at all othertimes.

Synchronous Sequential Circuits

Example 1 – Sequence Detector

Synchronous Sequential Circuits

Example 1 – Sequence Detector

Assign binary values to each state if the state table containsletter symbols.

How many state variables are needed to represent the fourstates?