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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
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Synchronous Sequential 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
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
used.
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
The primary inputs (W)
The present (current) outputs of the flip-flops (Q)
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.
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
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
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
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
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?
