STEM Success Center
CS 231
Handout
Guide To The K-Map (Karnaugh Map)
In many digital circuits and practical problems we need to find expression with minimum
variables. We can minimize Boolean expressions of 2, 3, or 4 variables very easily using the K-
map without using any Boolean algebra theorems. The K-map can take two forms Sum of
Product (SOP) and Product of Sum (POS) according to the needs of the problem. The K-map is
table-like representation but it gives more information than TRUTH TABLE. We fill the grid of K-
map with 0โs and 1โs then solve it by making groups.
Steps to solve expression using the K-map
1. Select K-map according to the number of variables.
2. Identify minterms or maxterms as given in the problem.
3. For SOP put 1โs in blocks of K-map respective to the minterms (0โs elsewhere).
4. For POS put 0โs in blocks of K-map respective to the maxterms(1โs elsewhere).
5. Make rectangular groups containing total terms in power of two like 2,4,8 ..(except 1)
and try to cover as many elements as you can in one group.
6. From the groups made in step 5 find the product terms and sum them up for SOP form.
The K-map Fill Order
2 - Variable Map
3- Variable Map
4 - Variable Map
A\B
0
1
0
0
1
1
2
3
A\BC
00
01
11
10
0
0
1
3
2
1
4
5
7
6
AB\CD
00
01
11
10
00
0
1
3
2
01
4
5
7
6
11
12
13
15
14
10
8
9
11
10
Grouping Rules
The Karnaugh map uses the following rules for the simplification of expressions by grouping
together adjacent cells containing ones
1. No zeros allowed.
2. No diagonals.
3. Only power of 2 number
of cells in each group.
4. Groups should be as
large as possible.
5. Everyone must be in at
least one group.
6. Overlapping allowed.
7. Wrap around is allowed.
8. Get the fewest number
of groups possible.
