Page 146 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 8: Memory

the same dimensions. Typically, however, PLAs have many more AND gates and so, for a PAL, Notes
the number of links would typically be many times more than the number for a comparable PLA.
8.8 Use of PAL and PLA in Combinational Circuit

The elements of Boolean algebra (two-element “switching algebra”) and how the operations in
Boolean algebra can be represented schematically by means of gates (primitive devices). How
switching expressions can be manipulated and represented in different ways was the subject
which also presented various ways of implementing such representations in a variety of circuits
using primitive gates.
With all of the tools for the purpose now in hand, The design of more complex logic circuits.
Circuits in which all outputs at any given time depend only on the inputs at that time are called
combinational logic circuits. The design procedures will be illustrated with important classes of
circuits that are now universal in digital systems.
The approach taken is to examine the tasks that a combinational logic circuit is instated to perform
and then identify one or more circuits that can perform the task. One circuit may have some
specific advantages over others, but it may also have certain deficiencies. Often one factor can
be improved, but only at the expense of others. Some important factors are speed of operation,
complexity or cost of hardware, power dissipation, and availability in prefabricated units. We
will take up a number of different operations that are useful in different contexts and show how
appropriate circuits can be designed to carry out these operations.

During the reprogramming procedure, power to the module and
reprogramming tool must not be interrupted.

8.8.1 Combinational Circuit Implementation with PLA

When implementing combinational circuit using PLA, we must reduce the number of product
terms. Number of literals in each product term is not important because all variables and their
complements are available.
In order to reduce the number of product terms, we have to simplify the functions and their
complements in order to fine the combination that result in the minimum number of product terms.
The size of the PLA is determined by the number of inputs, Number of product terms and the
number of outputs.

Implement the following two Boolean functions using a PLA.

F (A, B, C) = S(0, 1, 2, 4) and F (A, B, C) = S(0, 5, 6, 7)
1
2
First, we simplify the functions and their complements
F = A′B′ + A′C′ + B′C′
1

and F′ = AB + AC + BC
1
F = AB + AC + A′B′C′
2

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