The Karnaugh map for a Boolean function is given as The simplified Boolean…
2016
The Karnaugh map for a Boolean function is given as
The simplified Boolean equation for the above Karnaugh Map is
- A.
\(AB + CD + A\bar{B} + AD\) - B.
\(AB + AC + AD + BCD\) - C.
\(AB + AD + BC + ACD\) - D.
\(AB + AC + BC + BCD\)
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Correct answer: B
Simplified Boolean expression: AB + AC + AD + BCD
Derivation from the Karnaugh map:
Group the four ones in the row where A = 1 and B = 1. This 4-cell horizontal block eliminates C and D, giving the implicant AB.
Group the four ones in the column(s) where A = 1 and C = 1. This 4-cell block eliminates B and D, giving the implicant AC.
Group the four ones in the positions where A = 1 and D = 1. This 4-cell block eliminates B and C, giving the implicant AD.
After those maximal groups are taken, one remaining isolated 1 at B = 1, C = 1, D = 1 must be covered by the minterm BCD.
Putting the implicants together yields the minimal sum-of-products: AB + AC + AD + BCD
Note: Overlaps between groups are allowed and expected; they help to form the largest possible groups and thus produce the simplest expression.
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