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Chapter 13 Boolean Algebra Solutions

Question - 31 : -
Verify the following using Boolean Laws.
X + Y’ = X. Y + X. Y + X’. Y

Answer - 31 : -

L. H. S.
= X + Y’
= X. (Y+Y’) + (X + X’). Y’
= X. Y + X. Y’ + X. Y’ + X’. Y’
= X. Y + X. Y’ + X’. Y’
= R. H. S
OR
= X. Y + X. Y’ + X’. Y’
= X. (Y + Y’) + X’. Y’
= X. 1 + X’. Y’
= X + X’. Y’
= X + Y
= L. H. S

Question - 32 : - State Distributive law and verify it using truth table.

Answer - 32 : -

Distributive law : This law states that
(i) x(y + z) = xy + x.z.
(ii) x + yz = (x + y)(x + z)

Question - 33 : - Write Product of Sum expression of the function F (a, b, c, d) from the given truth table

Answer - 33 : -

F (a, b, c, d) =
(a + b + c + d).(a + b + c + d’). (a + b’ + c + d) . (a + b’ + c’ + d’). (a’ +b + c + d).
(a’ + b + c + d’). (a’ + b’ + c + d). (a’ + b’ + c + d’) . (a’ + b’ + c’ + d)

Question - 34 : -
Convert the following boolean expression inti! its equivalent Canonical Sum of Products form (SOP) :
(U + V + W) (U + V + W’) (U’ + V + W) (U’ + V’ + W’)

Answer - 34 : -

π (0,1, 4, 7)
∑(2, 3, 5, 6)
010 011 101 110
= U’VW’ + U’VW + UV’W + UVW’

Question - 35 : - Write the Product of Sum form of function G(U, V, W) for the following truth table representation of G 

Answer - 35 : -


Question - 36 : - Write the Sum of Product form of the function F(A, B, C) for the following truth table reprsentation of

Answer - 36 : -


SOP = A’BC’ + A’BC + AB’C’ + ABC

Question - 37 : -
Obtain the minimal SOP form for the following Boolean expression using K-Map.
F(A,B,C,D) = ∑ (0,2,3,5,7,8,10,1143,15)

Answer - 37 : -


Quad 1 = m0 + m2 + m8 + m10 = B’D’
Quad 2 = m3 + m7 + m15 + m11 = CD
Quad 3 = m5 + m7 + m15 + m13 = BD
Minimal SOP = B’D’ + CD + BD

Question - 38 : -
Reduce the following Boolean expression using
K-Map :
F(A,B,C,D) = 7r (0,1,2,4,5,6,8,10)

Answer - 38 : -


F(A, B, C, D) = π(0,1,2,4, 5, 6,8,10) F = (A + C).(A + D).(B + D)

Question - 39 : -
Reduce the following using K-Map :
F (A, B,C,D) = ∑(1,3,4,5,6,7,12,13)

Answer - 39 : -


Question - 40 : -
Reduce the following Boolean Expression using
K-Map :
F (A, B, C, D) = ∑(2, 3,4,5, 6, 7,8,10,11)

Answer - 40 : -


F (A, B, C, D) = A’B +A’C + B’C + ABD’

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