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Computer Science

Reduce the following boolean function with the help of Karnaugh's map:

F (a, b, c, d) = Σ (1, 2, 3, 11, 12, 14, 15)

Boolean Algebra

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Answer

Karnaugh map for Understanding ISC Computer Science Boolean Algebra Chapter 1 Unit 2 Question 7a Solution

From Pair (1,3):
Rows representing the pair: a'b'
Columns representing the pair: c'd + cd = d
Term Obtained = a'b'd

From Pair (3,2):
Rows representing the pair: a'b'
Columns representing the pair: cd + cd' = c
Term Obtained = a'b'c

From Pair (12,14):
Rows representing the pair: ab
Columns representing the pair: c'd' + cd' = d'
Term Obtained = abd'

From Pair (15,11):
Rows representing the pair: ab + ab' = a
Columns representing the pair: cd
Term Obtained = acd

Pairs (15,14) and (3,11) are redundant

Simplified expression = a'b'd + a'b'c + abd' + acd

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