The simplified Karnaugh maps are F(A, B, C) = A’B’ + AC , F(A, B, C) = C + AB’, F(A, B, C) = C’.
What are Karnaugh Maps ?
A Karnaugh map can be compared to a more advanced version of a truth table
In a K-map there are all the possible input variables and outcomes stored in cells.
It is a method to simplify and optimize Boolean expressions.
(a) m0 +m1+ m5+m7
Mapping the given function in a Karnaugh map,
The image is attached with the answer.
we can see two pairs
Pair-1 is m0 + m1
and Pair-2 is m5 + m7
= A’B’C’ + A’B’C + AB’C + ABC
= A’B’(C’ + C) + AC(B’ + B)
= A’B’ + AC
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = A’B’ + AC.
(b) F(1,3,5,4,7)
On Mapping the given function in a Karnaugh map, we will see
1 Pair and 1 Quad
Pair is m4 + m5
Quad is m1 + m3 + m5 + m7
= A’B’C + A’BC + AB’C + ABC + AB’C’ + AB’C
= A’C(B’ + B) + AC(B’ + B) + AB’(C’ + C)
(B +B' ) = 1 , (C’ + C) = 1
= A’C + AC + AB’
= C(A’ + A) + AB’
= C + AB’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C + AB’.
(c) m0+m2+m4+m6.
On Mapping the given function in a Karnaugh map, we will see
2 Pairs
Pair-1 is m0 + m4
Pair-2 is m2 + m6
= A’B’C’ + AB’C’ + A’BC’ + ABC’ = B’C’(A’ + A) + BC’(A’ + A)
= B’C’ + BC’
= C’(B’ + B)
= C’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C’.
(d) (0,2,4,6)
It will have the same expression as that of Option (c)
To know more about Karnaugh Maps
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