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Chapter 13 Boolean Algebra Solutions

Question - 41 : -
Verify the following using Boolean Laws :
A ‘ + B’ . C=A’ . B ‘ . C ‘ + A’ . B . C ‘ + A’ .B.C + A’ .B’ .C+ A.B’ .C

Answer - 41 : -

A’+ B’C = A’B’C’ + A,BCI + A’BC’ + A’BC + A’B’C + ABC
=A’C'(B’+B)+A’C (Grouping)
(B+B’)+AB’C
=> A’C’+ A’C + AB’C
(x+x’y=x+y)
=> A’ (C+C’ ) +AB’ C
=> A’+AB’C
(x+x’=1)
=> A’+B’C
X=A’ y=B’C
= LHS
Hence Proved.

Question - 42 : - Write the Boolean Expression for the result of the Logic Circuit as shown below :

Answer - 42 : -

F =(u+v’).(u+w).(v+w’)

Question - 43 : -
Reduce the following Boolean Expression to its simplest form using K-Map :
F (X, Y, Z, W)
∑(2,6,7,8,9,10,11,13,14,15)

Answer - 43 : - ∑(2,6,7,8,9,10,11,13,14,15)

F = XY’ + ZW’+ XW + YZ

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