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Digital Electronics
Truth table
A
0
0
1
1
B
0
1
0
1
Y
0
1
1
1
Sum-of-products K-map
B
A
A
B
1
1
1
Product-of-sums K-map
B
A
A
B
1
Figure 6.10 Two-variable Karnaugh maps.
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
Y
1
0
1
0
1
0
1
0
Sum-of-products K-map
BC BC BC
A
A
1
1
1
1
BC
Product-of-sums K-map
B+C B+C B+C
A
A
1
1
1
1
B+C
Figure 6.11 Three-variable Karnaugh maps.
Figure 6.12 shows the truth table, minterm Karnaugh map and maxterm Karnaugh map of the fourvariable Boolean function
Y = AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD (6.48)
Y = A + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DD
A + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DD
(6.49)
To illustrate the process of forming groups and then writing the corresponding minimized Boolean
expression, Figs 6.13(a) and (b) respectively show minterm and maxterm Karnaugh maps for the
Boolean functions expressed by equations (6.50) and (6.51). The minimized expressions as deduced
from Karnaugh maps in the two cases are given by Equation (6.52) in the case of the minterm Karnaugh
map and Equation (6.53) in the case of the maxterm Karnaugh map:
Y = AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD (6.50)
Y = A + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DD
A + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DDDDA + B + C + DD (6.51)
Y = BBD + BBD
(6.52)
Y = DDDA + BB
(6.53)