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Analogue and digital electronics theory 2/49

=AB +AB

A

1

Figure 2.102 NOR realization of the exclusive-OR function

state-recording device which may subsequently be referred to
during various interrupt operations.
2.3.26 The Marnaugh map
The Rarnaugh map provides an alternative representation of a
Boolean expression for all possible Boolean input combina-
tions. In some respects the Karnaugh map is like a truth table
in that identical logical expressions display an identical pattern
on a Karnaugh map. The Karnaugh map, however, also has a
great utility in simplifying Boolean expressions in a systematic
manner.
The Karnaugh map consists of a set of boxes in which each 11
box represents one possible combination of the Boolean input
variables. The boxes are assigned either a ‘I’ or a ‘0’ to -_
indicate the value of the Boolean expression for the particular IO 1 ABCD i ABCD 1 ABCD 1 ABCD
combination of input variables that the box represents. The
number of boxes required is 2”, where n is the total number of ~ ~~~ ~~
input variables. Although any number of input variables can Figure 2.103 Karnaugh map for a four-input system
be represented, a practical limitation is about seven. Figure
2.103 shows the Karnaugh map for a four-input system.
Within teach box the unique Boolean input combination is in Figure 2.104. The maps are drawn up by placing a ‘1’ in each
represented by assigning each variable the logic values indi- box for which the combination of input variables makes the
cated along the horizontal and vertical axes. These values logical expression have a value of 1. All the other boxes
conform to the binary Gray code in which adjacent consecut- represent the combination of input variables which make the
ive characters differ only in one variable. This imparts a expression have a logical value of 0. Usually the ‘0’ is not
property to the Karnaugh map in that the adjacent squares entered in the box.
(vertically or horizontally) differ only in one variable, A second example for consideration is
Asan examgle, The Boolean expression, F = ABCD +
ABCD -t ABCD is represented by the Karnaugh map given F = ABCD + AC + CD