Page 86 - C++

6 (a) State any one Distributive Law of Boolean Algebra and Verify it using (2)
truth table.

Ans. Distributive Law:
A+BC=(A+B)(A+C)
Verification

A B C BC A+BC (A+B) (A+C) (A+B)(A+C)
0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0
0 1 0 0 0 1 0 0
0 1 1 1 1 1 1 1
1 0 0 0 1 1 1 1
1 0 1 0 1 1 1 1
1 1 0 0 1 1 1 1
1 1 1 1 1 1 1 1

OR
A(B+C)=AB+AC

A B C B+C A(B+C) AB AC AB+AC
0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0
0 1 0 1 0 0 0 0
0 1 1 1 0 0 0 0
1 0 0 0 0 0 0 0
1 0 1 1 1 0 1 1
1 1 0 1 1 1 0 1
1 1 1 1 1 1 1 1

(1 Mark for stating any one Distributive Law correctly)
(1 Mark for correctly verifying the stated Law using Truth Table)

(b) Draw the Logic Circuit of the following Boolean Expression: (2)
((U + V’).(U + W)). (V + W’)

Ans.

(c) Derive a Canonical SOP expression for a Boolean function F(X,Y,Z) (1)
represented by the following truth table:

22