Lec 08 - DESIGN PROCEDURE

DESIGN PROCEDURE
D.R.V.L.B Thambawita
October 29, 2017
D.R.V.L.B Thambawita DESIGN PROCEDURE
https://sites.google.com/view/vajira-thambawita/leaning-materials/slides

DESIGN PROCEDURE
Design procedures or methodologies specify hardware that will
implement a desired behavior.
The design effort for small circuits may be manual, but
industry relies on automated synthesis tools for designing
massive integrated circuits.
The design of a clocked sequential circuit starts from a set of
specifications and culminates in a logic diagram or a list
of Boolean functions from which the logic diagram can be
obtained.
In contrast to a combinational circuit, which is fully specified
by a truth table, a sequential circuit requires a state table for
its specification.
The first step in the design of sequential circuits is to obtain a
state table or an equivalent representation, such as a state
diagram.

DESIGN PROCEDURE
1 From the word description and specifications of the desired
operation, derive a state diagram for the circuit.
2 Reduce the number of states if necessary.
3 Assign binary values to the states.
4 Obtain the binary-coded state table.
5 Choose the type of flip-flops to be used.
6 Derive the simplified flip-flop input equations and output
equations.
7 Draw the logic diagram.

DESIGN PROCEDURE: Example
Suppose we wish to design a circuit that detects a sequence of
three or more consecutive 1’s in a string of bits coming through an
input line (the input is a serial bit stream).

We need to assign binary codes to the states and list the state
table.
We choose two D ﬂip-ﬂops to represent the four states, and
we label their outputs A and B .
There is one input x and one output y.

The characteristic equation of the D flip-flop is Q(t +1) = DQ
Which means that the next-state values in the state table
specify the D input condition for the flip-flop.
The flip-flop input equations can be obtained directly from
the next-state columns of A and B and expressed in
sum-of-minterms form as
A(t + 1) = DA(A, B, x) = (3, 5, 7)
B(t + 1) = DB(A, B, x) = (1, 5, 7)
y(A, B, x) = (6, 7)

The Boolean equations are simplified by means of the maps
plotted in the following figure.
DA = Ax + Bx
DB = Ax + B x
y = AB
The advantage of designing withD flip-flops is that the Boolean
equations describing the inputs to the flip-flops can be obtained
directly from the state table.

Figure: Moore type circuit

Excitation Tables
When D -type flip-flops are employed, the input equations are
obtained directly from the next state.
This is not the case for the JK and T types of flip-flops.
It is necessary to derive a functional relationship between the
state table and the input equations.
The flip-flop characteristic tables are useful for analyzing
sequential circuits and for defining the operation of the
flip-flops.
During the design process, we usually know the transition
from the present state to the next state.
Wish to find the flip-flop input conditions that will cause the
required transition.
we need a table that lists the required inputs for a given
change of state. Such a table is called an excitation table .

Excitation Tables
Do you remember?
Figure: Characteristic Tables

Excitation Tables
Figure: Flip-Flop Excitation Tables

Synthesis Using JK Flip-Flops
Example:
Figure: State Table and JK Flip-Flop Inputs

Example:JK ﬂip-ﬂop
Figure: Maps for J and K input equations

Example:JK flip-flop
Figure: Logic diagram for sequential circuit with JK flip-flops

Synthesis Using T Flip-Flops
Figure: State diagram of three-bit binary counter

Figure: State Table for Three-Bit Counter

Figure: Maps for three-bit binary counter

Figure: Logic diagram of three-bit binary counter

Lec 08 - DESIGN PROCEDURE

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Lec 08 - DESIGN PROCEDURE