Boolean Algebra and Simplification Techniques
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AB
CD
AB
AB
CD
CD
AB
CD
AB
CD
AB
AB
CD
CD
AB
CD
A
C
C
A
D
B
B
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CD
00
00
01
11
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01
11
10
Figure 6.9 Different styles of row and column identification.
Having accounted for groups with all 1s, the minimum ‘sum-of-products’ or ‘product-of-sums’
expressions can be written directly from the Karnaugh map.
Figure 6.10 shows the truth table, minterm Karnaugh map and maxterm Karnaugh map of the
Boolean function of a two-input OR gate. The minterm and maxterm Boolean expressions for the
two-input OR gate are as follows:
Y = A + B (maxterm or product-of-sums)
(6.44)
Y = AAB + AAB + AAB (minterm or sum-of-products)
(6.45)
Figure 6.11 shows the truth table, minterm Karnaugh map and maxterm Karnaugh map of the threevariable Boolean function
Y = AABBC + AABBC + AABBC + AABBC
(6.46)
Y = A + B + CCCCA + B + CCCCA + B + CCCCA + B + CC
(6.47)