What is the minimal form of the Karnaugh map shown below? Assume that X…
2012
What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term.
- A.
\(\bar{b} \bar{d}\) - B.
\(\bar { b } \bar { d } + \bar{b} \bar{c}\) - C.
\(\bar{b} \bar{d} + {a} \bar{b} \bar{c} {d}\) - D.
\(\bar{b} \bar{d} + \bar{b} \bar{c} + \bar{c} \bar{d}\)
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Correct answer: B
Correct. Using don't-cares you can form two 4-cell groups: one covering b=0 and d=0 → ~b~d (m0, m2, m8, m10), and one covering b=0 and c=0 → ~b~c (m0, m1, m8, m9). Together they cover every 1, giving the minimal expression ~b~d + ~b~c (which factors to ~b(~c + ~d)).
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