Low Order Thinking Questions: (Boolean Algebra)
1.
State and verify absorption law in Boolean algebra.
Ans. Absorption Law states that :
a.
X+XY=X b. X(X+Y)=X
2.
Verify X’.Y+X.Y’=(X’+Y’).(X+Y) algebraically.
Ans. LHS = X’Y + XY’
= (X’+X) (X’+Y’) (Y+X) (Y+Y’)
= 1.(X’+Y’) (X+Y).1
= (X’+Y’) (X+Y)
= RHS, hence proved
3.
Write the equivalent Boolean Expression F for the following circuit diagram
:
Ans.: A’B+AB+B’C
4.
If F(P,Q,R,S) = Π (3,4,5,6,7,13,15) , obtain the simplified form using
K-Map.
Ans.:
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R+S
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R+S’
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R’+S’
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R’+S
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P+Q
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0
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P+Q’
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0
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0
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0
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0
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P’+Q’
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0
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0
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P’+Q
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Reduction of groups following the
reduction rule :
Quad1 = M4.M5.M6.M7 =
P+Q’
Quad2 = M5.M7.M13.M15 = Q’+S’
Pair = M3.M7 =
P+R’+S’
Therefore POS of F(P,Q,R,S) =
(P+Q’)(Q’+S’)(P+R’+S’)
5.
F(a,b,c,d)=Σ(0,2,4,5,7,8,10,12,13,15)
F(a,b,c,d) = B1 + B2 + B3
B1 =
m0+m4+m12+m8 = c’d’
B2 = m5+m7+m13+m15 = bd
B3 = m0+m2+m8+m10 = b’d’
F(a,b,c,d) = c’d’ + bd +
b’d’
6.
Write the equivalent Boolean expression for the following logic circuit:
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X
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Y
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Z
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F
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0
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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0
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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· Express in the product of sums
form, the Boolean function F(X,Y,Z), the truth table for which is
given below:
1/2 Marks Practice Questions:
1. State and Prove
DeMorgan Law using Truth Table
2. State and prove
Absorption Law algebraically.
3. State and Prove
Distributive Law algebraically.
4.
Write the equivalent Boolean Expression for the following
Logic Circuit 2
5.
Write the equivalent Boolean Expression F for the following circuit diagram
: 2
6.
Write the equivalent Boolean Expression F for the following circuit diagram
: 2
7.
Convert the following Boolean expression into its equivalent Canonical Sum
of Product Form((SOP)
(X’+Y+Z’).(X’+Y+Z).(X’+Y’+Z).(X’+Y’+Z’) 1
8.
Convert the following Boolean expression into its equivalent Canonical
Product of Sum form (POS):
A.B’.C + A’.B.C +A’.B.C’ 1
9.
Draw a Logical Circuit Diagram for the following Boolean expression:
A.(B+C’) 2
10.
Write the equivalent Boolean Expression F for the following circuit
diagram: 2
11.
Prove that XY+YZ+YZ’=Y algebraically 2
12.
Design (A+B).(C+D) using NOR Gate. 2
3 Marks Practice Questions
13.
If F(a,b,c,d)=Σ(0,2,4,5,7,8,10,12,13,15), obtain the simplified form using
K-Map.
14.
If F(a,b,c,d) =Σ(0,3,4,5,7,8,9,11,12,13,15), obtain the simplified form
using KMap
15.
Obtain a simplified form for a boolean expression
F(U,V,W,Z)= π
(0,1,3,5,6,7,10,14,15)
16.
Reduce the following boolean expression using K-Map
F(A,B,C,D) =
Σ(5,6,7,8,9,12,13,14,15)
