1
EC262 Topic 6: The Four-Input Karnaugh Map
The extension of three-input K-maps to four-input K-maps is quite straightforward.
Four-Input Karnaugh Maps
A digital logic circuit with four separate inputs (let’s call them
A
,
B
,
C
and
D
) has
4
2
16
=
possible input
combinations: 0000, 0001, …, 1110, 1111. In other words, the truth table for this circuit will have 16 lines.
Each of these possible input combinations represents a minterm. For instance, the input combination 0101
represents the minterm :
There will, of course, be an output for each of the sixteen possible input minterm combinations.
The K-map for a four-input problem is a table where the rows and columns (together) account for all possible
inputs to logic circuit. The outputs are displayed in a four-input K-map that is organized as follows:
AB
CD
00
01
11
10
00
01
11
10
Note that the rows and columns are arranged in the order from left to right (and from top to bottom) as:
00 01 11 10
.
Take a moment to memorize this order.
Note that the order is
NOT
00
01
10
11 .
Exactly as with the three-input K-map, the entry in each table cell of the four-input K-map corresponds to the
output for the inputs specified by the row and column.
Within each of the sixteen squares of the K-map, we
place the output (0 or 1) that corresponds to the input minterm.
From
Introduction to Logic Design
, Alan Marcovitz, McGraw Hill, 2010
Example.
Suppose a digital logic circuit with three inputs (
x
,
y
,
z
) has the following Boolean expression:

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