Basic idea about K-Map

1. NAME ID
Islam, Md. Arafatul 14-26696-2
Islam, Mohammad Kamrul 14-26664-2

3. The Karnaugh Map provides a simple and straight forward
method of minimizing Boolean expression.

4. Map the following expression into a k-map:
• A’BC+AB’C’+ABC
• (P+Q+R)(P’+Q’+R)(P’+Q+R)

5. If there are 3 variables A,B and
C then A and B should be used
to name the row and C to name
the columns.
C
AB

6. Only one variable
changes from R1
to R2, R2 to R3
and R3 to R4.
CAB 0 1
00
01
11
10

7. You can put 0’s in
the remaining
cells or leave
them blank.
C
AB
0 1
00
01
11
10
1
1
1
0 1 1 1 0 0 1 1 1

8. You can put 1’s in
the remaining
cells or leave
them blank.
C
AB
0 1
00
01
11
10
0
0
0
0 0 0 1 1 0 1 0 0

9. Karnaugh maps reduce logic functions.
Most simplified equations
Its fast and easier compared to Boolean algebra.
Lowest cost

10. Minimize the following expression using K-Map
AB’C+A’BC+A’B’C+A’B’C’+AB’C’
Circuit Design Before K-MAP Grouping
5 AND Gates
and
3 NOT Gates

11. STEP 1: The 1’s in adjacent cells can be grouped together
STEP 2: The no. of cells in a group can be 1,2,4… i.e 2^n (n=0,1,2…)
STEP 3: The GOAL is to always try to maximize the
group size and minimize no. of groups.
STEP 4: Overlapping can be done if it helps to
increase group size
STEP 5: Each 1 in the K-Map must be in at least
one group or the other

12. Simplified SOP
expression =
C
AB
0 1
00
01
11
10
1
1
1 1
1
A’C
B’
+
1 0 1 0 1 1 0 0 1 0 0 0 1 0 0

13. Circuit Design After K-MAP Grouping
1 NAND Gate
1 NOR Gate
and
1 NOT Gate