Simplify the following using K-Map \(\mathrm{F}(\mathrm{A}, \mathrm{B},…
2022
Simplify the following using K-Map
\(\mathrm{F}(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D})=\sum(0,2,5,7,8,10,13,15)\)
- A.
\(\mathrm{BD}+\mathrm{B}^{\prime} \mathrm{D}^{\prime}\) - B.
\(\mathrm{AC}+\mathrm{A}^{\prime} \mathrm{C}^{\prime}\) - C.
\(\mathrm{BC}+\mathrm{B}^{\prime} \mathrm{C}^{\prime}\) - D.
\(\mathrm{AD}+\mathrm{A}^{\prime} \mathrm{D}^{\prime}\)
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Correct answer: A
We have F(A,B,C,D) = Σ(0, 2, 5, 7, 8, 10, 13, 15). Place these minterms on a 4-variable K-map and look for groups of four.
Key grouping observations:
Minterms 5, 7, 13, 15 all have B = 1 and D = 1, so they group to give the product term BD.
Minterms 0, 2, 8, 10 all have B = 0 and D = 0, so they group to give the product term B' D'.
Combining the groups yields the simplified sum-of-products:
F = BD + B' D'.
Note: This expression can also be recognized as the XNOR of B and D (i.e., true when B = D).
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