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Boolean Algebra

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Question
CBSEENCO12011552
Wired Faculty App

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

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Question
CBSEENCO12011553
Wired Faculty App

Draw the Logic Circuit of the following Boolean Expression using only NAND Gates:
X.Y + Y.Z

Solution

Draw the Logic Circuit of the following Boolean Expression using only

Question
CBSEENCO12011554
Wired Faculty App

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

Solution

F(U,V,W)= U’V’W’ + U’VW’ + U’VW + UVW’

Question
CBSEENCO12011555
Wired Faculty App

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)

Solution

Reduce the following Boolean Expression to its simplest form using K-M

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