# Switching Circuits Questions and Answers – Boolean Expressions and Truth Tables

This set of Switching Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Expressions and Truth Tables”.

1. What is the correct order of operations to be performed, assuming that there are no parenthesis?
a) Complementation, followed by AND and then OR
b) OR, followed by Complementation and then AND
c) AND, followed by Complementation and then OR
d) Complementation, followed by OR and then AND

Explanation: The correct order of operations is Complementation, followed by AND and then OR. The reason for this is that the Unary operator has the highest precedence. AND is performed before OR because AND is called as logical multiplication and OR is known as logical addition. As multiplication is always performed before addition, AND is performed before OR operation.

2. How many rows will a truth table for an n-variable expression have?
a) n
b) n2
c) 2n
d) 2n

Explanation: Because the expression has n variables, and each variable can have the value 0 or 1, the
number of different combinations of values of the variables is
2 × 2 × . . . = 2n times.

3. The following is the truth table of a 2 input OR gate, whose inputs are A and B and output is Y.

A B Y
0 0 0
0 1 1
1 0 1
1 1 1

a) True
b) False

Explanation: The OR gate outputs 0 only when all of its inputs are 0. In other words, the OR gate outputs 1 when at least one of its inputs is 1.

4. Find the Boolean expression corresponding to the digital circuit given below.

a) ((A + B).C’)’
b) (A.B + C’)’
c) (A + B).C’
d) A + B.C’

Explanation: The output of the OR gate is (A + B). This is ANDed with C’. Hence the output becomes (A + B).C’. This is passed to the input of an inverter. Thus, the final output is ((A + B).C’)’.

5. Find the Boolean expression corresponding to the digital circuit given below.

a) A + B + C’ + D.E
b) (A + B) + (C’.D.E)’
c) A.B + C + D. E
d) A.B + C’.DE

Explanation: A and B are the inputs to the OR gate, the output is (A + B). This is one of the inputs to the second OR gate. The other input is the output of the NOT gate. The input to the NOT gate is C’.D.E. Hence the output is (A + B) + (C’.D.E)’.

6. Find the Boolean expression corresponding to the digital circuit given below.

a) A.B
b) A’ + B’
c) (A + B)’
d) (A.B)’

Explanation: The output of OR gate is given to a NOT gate. Hence the output is (A + B)’.

7. The following is the truth table of a 2 input AND gate, whose inputs are A and B and output is Y.

A B Y
0 0 0
0 1 0
1 0 0
1 1 1

a) True
b) False

Explanation: The AND gate outputs 1 only when all of its inputs are 1. In other words, the AND gate outputs 0 when at least one of its inputs is 0.

8. Find the Boolean expression corresponding to the digital circuit given below.

A B Y
0 0 1
0 1 1
1 0 1
1 1 0

a) A + B
b) A.B
c) (A + B)’
d) (A.B)’

Explanation: The output is 0 only when both inputs are 1. This is the complement of AND gate. Hence the Boolean Expression is (A.B)’.

9. Find the Boolean expression corresponding to the digital circuit given below.

a) A + B
b) A.B
c) A’ + B’
d) (A + B)’

Explanation: The inputs to the OR gate are the outputs from the NOT gates, i.e., A’ and B’. Hence the output is A’ + B’.

10. What specifies the values of a Boolean expression for every possible combination of values of the variables in the Boolean expression?
a) Karnaugh map
b) Truth table
c) Circuit diagram
d) Logic diagram

Explanation: The truth table specifies the values of a Boolean expression for every possible combination of values of the variables in the Boolean expression. The name truth table comes from a similar table which is used in symbolic logic to list the validity or falsity of a statement under all possible conditions.

11. Identify the Boolean expression corresponding to the truth table given below.

A B Y
0 0 1
0 1 0
1 0 0
1 1 0

a) A + B
b) A.B
c) A’ + B’
d) (A + B)’

Explanation: The output is 1 only when both inputs are 0. This is the complement of the output of the OR gate. Hence the Boolean expression is (A + B)’.

12. Identify the Boolean expression corresponding to the truth table given below.

A B Y
0 0 1
0 1 0
1 0 0
1 1 1

a) A + B
b) A.B
c) A’ + B’
d) A.B + A’.B’

Explanation: The output is 1 only when either both inputs are 0 or both inputs are 1. That is when A.B is 1 or A’.B’ is 1. Thus the Boolean expression is A.B + A’.B’. This can also be observed from the below table.

A B A.B A’ B’ A’.B’ A.B + A’.B’ Y
0 0 0 1 1 1 1 1
0 1 0 1 0 0 0 0
1 0 0 0 1 0 0 0
1 1 1 0 0 0 2 1

.

13. Identify the Boolean expression corresponding to the truth table given below.

A Y
0 1
1 0

a) A
b) A.A
c) A’ + A
d) A’

Explanation: The output is 1 only when the input is 0 and the output is 0 when the input is 1. This corresponds to a NOT gate. Hence the corresponding Boolean expression is A’.

14. Identify the Boolean expression corresponding to the digital circuit given below.

a) A’.B’
b) A.B
c) A’ + B’
d) (A’.B’)’

Explanation: The inputs to the AND gate are the outputs of 2 NOT gates. Hence the output of the AND gate is A’.B’. As this is the input of a NOT gate the corresponding Boolean expression is (A’.B’)’.

15. Identify the Boolean expression corresponding to the digital circuit given below.

a) A’.B’
b) A.B
c) A’ + B’
d) A’.B’ + A.B

Explanation: The inputs to the first AND gate are the outputs of 2 NOT gates. Hence the output of the AND gate is A’.B’. The output of the second AND gate is A.B. The output of AND gates is given to OR gate. Thus the corresponding Boolean Expression is A’.B’ + A.B.

Sanfoundry Global Education & Learning Series – Switching Circuits.

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