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Boolean Algebra

Question

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State Distributive Laws of Boolean Algebra and verify them using truth table.

(i) X. (Y+Z)= X.Y + X.Z
(ii) X + Y.Z= (X + Y). (X+Z)

Solution

(i)

X	Y	Z	Y+Z	X.(Y+Z)	X.Y	X.Z	X.Y+X.Z
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

(ii)

X	Y	Z	Y.Z	X+Y.Z	(X+Y)	(X+Z)	(X+Y).(X+Z)
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

Some More Questions From Boolean Algebra Chapter

Derive a Canonical SOP expression for a Boolean function F, represented by the following truth table:

U V W F(U,V,W)
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 0

Reduce the following Boolean Expression to its simplest form using K-Map:
F(X,Y,Z,W)= Σ (0,1,2,3,4,5,10,11,14)

State DeMorgan’s Laws of Boolean Algebra and verify them using truth table.

Draw the Logic Circuit of the following Boolean Expression using only NOR Gates:
( A+B).(C+D)

Derive a Canonical POS expression for a Boolean function G, represented by the following truth table:

X Y X G(X,Y,Z)
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 1

Reduce the following Boolean expression to its simplest form using K-Map:
E(U,V,Z,W)= Σ (2,3,6,8,9,10,11,12,13)

Verify the following using Boolean Laws.
A’+ B’.C = A’.B’.C’+ A’.B.C’+ A’.B.C + A’.B’.C+ A.B’.C

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

Derive a Canonical POS expression for a Boolean function F, represented by the following truth table:

P Q R F(P, Q, R)

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 0

1 0 1 0

1 1 0 1

1 1 1 1

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)

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