# QUESTION BANK – BOOLEAN ALGEBRA

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QUESTION BANK – BOOLEAN ALGEBRA

1) State and verify Absorption Laws. 2) Write the equivalent Boolean expression for the following Logic circuit.

NOTE :

OR GATE

3) Reduce the following Boolean expression using K-Map: F(U,V,W,Z) = (0,1,2,4,5,6,14,15) 4) Write the SOP and POS form of the function H(U,V,W). truth table representation of H is as follows.

U

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5) Verify X.Y’+Y’Z=X.Y’Z+XY’Z’+X’Y’Z algebraically.

6) Represent the Boolean Expression (X+Y) (Y+Z) (X+Z) with the help of NOR gate.

7) State and verify De-Morgan’s law in Boolean Algebra.

8) Draw the circuit diagram for F = AB’C + C’B using NAND gate only.

9) Write the SOP and POS form of the function G(U,V,W). Truth table representation of G is as follows:

U

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W

G

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10) Reduce the following Boolean expression using K -Map:F (A, B, C, D)=∑ (0, 1, 2, 3, 4, 5, 10, 11, 15) 11) Give the canonical SOP form of the following expression: XY+YZ+YZ’=Y 12) Draw the K-map for expression.F(X,Y,Z,W) = π (0, 1, 4, 5, 7, 8, 9, 12, 13, 15) 13) Design a circuit for the Boolean expression (A’ + B’ + C’) (A + B’ + C’) (A + B + C’)using NOR gate only. 14) Write the SOP and POS form of the function F(x, y, z). The truth table representation F is given below:

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x

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15) Prove (x+y)(x+z) = x+yz algebraically.

16) Give the canonical POS form for expression : (x+y’).(x’+z)

17) Write the equlvalent Boolean expression for the following logic

circuit:

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A NOR
B

NOR

C NOR
D

18) state and verify demorgan’s law and distributive law

19) Reduce the following Boolean expression using K-Map. F(a,b,c,d)=(1,4,5,8,9,12,13) 20) State and verity DeMorgan’s law algebraically. 21) Represent the Boolean expression x.y’ + y.z’ with the help of NAND gates only. 22) Obtain simplified form for following expression using K-Map.F(w, x, y, z) = ‫ ∑ﻗ‬(1, 3, 4, 5, 7, 9, 11, 12, 13, 15) 23) Write the POS form of a Boolean function F(u, v, w) which is represented in a truth table as follows:

U

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W

F

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24) State the principle of duality in Boolean algebra and give the dual of the Boolean expression (x+y).(x+z). 25) Given a Boolean function F= XY + X’Y’ + Y’Z Implement it with only NAND-to-NAND logic. 26) A Boolean function F defined on 3 input variables X,Y,Z is 1 if and only if number of 1 input is odd.
Draw the truth table for the above function and express it in canonical SOP and POS form. 27) Using Karnaugh map, obtain the simplified expression for (a) AND (b) K-Map:

WZ XY 00
1
1

01 11 10

0

0 1

1

1 1

WZ 0+0 0+1 1+1 1+0
XY 1+0

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00 1 1 01 1 0

1 1 1 1

0+0 0 1 0+1 0 0

11

1+1 0 0

10

1+0 0 1

28) State and verify De Morgan’s theorem. 29) Write the equivalent expression for the following logical circuit

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1 0 0 0 0 0 0 0

30) Express P’ + QR’ in canonical SOP form. 31) Reduce the following Boolean expression using K-Map:
F(P,Q,R,S)=∑(l,3,5,8,11,12,15 32) Express P+Q’R in canonical SOP form. 33) Reduce the following Boolean expression using K-Map.
F(P, Q ,R, S) = ∑ (0,3,5,6,7,11,12,15) 34) State and verify Associative Law. 35) Write the equivalent expression for the following logical circuit:

36) Express P+Q ’R in POS form. 37) Reduce the following Boolean expression using K-Map: F(P, Q, R, S) = π (0,3,5,6,7, 11, 12, 15)

38) Reduce the following Boolean expression using K-map.
F(A,B,C,D)= (0,1,2,4,5,7,8,9,10,11,14) 39) Prove that XY+YZ+YZ’=Y 40) Represent the following expression using NAND gate only:-
a) X’Y+Y’Z b) NOT GATE c) AND gate d) X(Y’+Z) e) (X+Y)(Y+Z)(X+Z) 41) Represent the following expression using NOR gate only:-

f) XY’+Z

g) OR gate

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a) X’Y+Y’Z b) NOT GATE c) AND gate d) X(Y’+Z) e) (X+Y)(Y+Z)(X+Z) f) XY’+Z g) OR gate

42) State the commutative laws and verify them usinf truth table.

43) Write the dual of the folowing expression:-

a) (B’+C).A b) AB’+C’D c) (A+BC+(AB’)) d) (X+Y)(X’+Z’)(Y+Z) e) (U+W)(V’U+W) f) (X+Y)’=X’.Y’

44) Seven inverters(NOT gate)are cascaded one after another. What is the output is input is 1. show with diagram.

45) Given the following circuit :-

What is the output if (i) both inputs are FALSE (ii) both inputs are TRUE (iii) one is FALSE and other is TRUE 49) What is the output if(i) both inputs are FALSE (ii)both inputs are TRUE (iii)one is FALSE and other is TRUE

50)

(a)

State and prove the Distributive law algebraically.

(b)

Write the equivalent POS expression of following SOP form

F (x,y,z)= ∑ (0,2,4,6)

(c)

Obtain the simplified form of a Boolean expression using K-Map.

F(a,b,c,d)=∑(0,1,2,3,4,7,11,12,14)

51) a) State De’Morgans law and verify one of the laws using truth table .

b) If F(w,x,y,z) =  (0,2,4,5,7,8,10,12,13,15) , obtain the simplified form using K-Map.

c) Represent AND using NOR gate(s).

d) Write the POS form of a Boolean function G, which is represented in a truth table as follows :

P

Q

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G

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e) State and verify Absorption law?

f) Write the equivalent Boolean Expression for the following logic circuit :

XY

F

52. a.
b. c.

Simplify the Boolean expression of F using Karnaugh Maps: F (a, b, c) =  (1, 3, 5, 7)
State and verify the De Morgan’s law using Algebraic method? Given the following truth table, write the sum-of-product form of the function F(x, y, z).

X

Y

Z

F

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0

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d. Represent NOT using only NOR gate(s).

53) (a) State Involution Law and verify the same using truth table.

(b) Write the Product of Sum form of the function F(x , y , z), truth table representation of

F is given below:

X

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F

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(c) Write the equivalent Boolean Expression for the following Logic Circuit.

A AND

C OR

AND

(d) Reduce the following Boolean Expression using K-Map F(A,B,C,D) = ∑ ( 0 , 2, 4, 5, 6, 7, 8, 10, 13, 15)
54) (a) State and verify De-Morgan’s, absorption Law in Boolean Algebra. (b) Draw the circuit diagram for F = AB’C + C’B using NAND to NAND logic only. (c) Write the Products of summand SOP form of the function G(U,V,W). Truth table representation of G is as follows:

U

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G

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(d) Reduce the following Boolean expression using K - Map : F (A, B, C, D) =

e) Write short note on principles of Duality. f) Prove algebraically (X + YZ) =(X+Y) (X+Z) g) A Boolean function F defined on three input variables A, B, C and is 1(one) if and if only if number of 0(zero) inputs is odd (e.g. F is 1(one) if A=0, B=1, C=1). Draw the truth table for the above function and express it in canonical sum of product form. h) Simplify the following Boolean expression using K-map :
F(A, B, C, D)=m0 + m1 + m4 + m5 + m7 + m8 55) Draw the diagram of digital circuit for the function
F(X,Y,Z)=(X+Y) . (X+Y) .(Y+Z) 56) (i) State the Distributive law and verify the law using a truth table.
(ii) Write the dual of the Boolean expression (AB`+A`B`C+AC) (iii) Draw the logic diagram of expression AB`C`+B`C+ABC,
using NAND Gates.

(iv) Write the output expression for the below logic circuit.

X Y Z

AND

AND

OR

AND

(v) Write the SOP form of the function H(a,b,c,d)=(m0, m2,m3,m6,m7,m8,m10).Simplify the expression by using the k-map.
58. a) Give Boolean expression for the logic diagram shown below. Also find out its outputs when a=1, b=1 and c=1. a

y b

c

b. Prove (A+B).(A’+C)=(A+B+C).(A’+B+C’).(A’+B+C).(A’+B’+C) Algebrically.

c. Given the following truth table, write the product of sums form of the function F(x,y,z) and draw k-map.

x y

z

F

0 0

0

0

0 0

1

1

0 1

0

1

0 1

1

0

1 0

0

1

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1 0

1

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1 1

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1 1

1

1

59. a) State the associative law and verify the law using truth table.

b) Prove XY+YZ+YZ’=Y, algebraically.

c) Obtain the Simplified form of a Boolean expression using Karnaugh map.

F(X,Y,Z,W) = Π (0, 1, 4, 5, 7, 8, 9, 12, 13, 15)

60. Reduce the following Boolean expression using K-Map

F(U,V,W,Z) = Π (0, 1, 2, 5, 8, 10, 11, 13, 14, 15)

61. Write the equivalent POS expression of following SOP for F (x,y,z)= ∑ (0,2,4,6)

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