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EC262 Topic 6: The FourInput Karnaugh Map
The extension of threeinput Kmaps to fourinput Kmaps is quite straightforward.
FourInput 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 Kmap for a fourinput problem is a table where the rows and columns (together) account for all possible
inputs to logic circuit. The outputs are displayed in a fourinput Kmap 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 threeinput Kmap, the entry in each table cell of the fourinput Kmap corresponds to the
output for the inputs specified by the row and column.
Within each of the sixteen squares of the Kmap, 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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''''
''
'
'
'
A B C D
A B CD
A BCD
ABC D
ABC D
ABCD
AB CD
+
+
+
+
++
What is the Kmap for this circuit?
AB
CD
00
01
11
10
00
01
11
10
So…what’s the plan?
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This note was uploaded on 03/27/2012 for the course ECE 200 taught by Professor Nasis during the Spring '08 term at Drexel.
 Spring '08
 NASIS

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