Boolean Algebra

Question 1

What is Boolean Algebra used for?

Answer 1

It is used to simplify and analyze logic circuits using binary values and logical operations.

Question 2

What is the output of the AND operation when both inputs are 1?

Answer 2

1

Question 3

What is the output of the OR operation when both inputs are 0?

Answer 3

0

Question 4

What is the NOT operation of 1?

Answer 4

0

Question 5

What is the Identity Law in Boolean algebra?

Answer 5

A + 0 = A and A · 1 = A

Question 6

What is the Null Law (Operations with Zero and 1) in Boolean algebra?

Answer 6

A + 1 = 1 and A · 0 = 0

Question 7

What is the Idempotent Law in Boolean algebra?

Answer 7

A + A = A and A · A = A

Question 8

What is the Complement Law in Boolean algebra?

Answer 8

A + A′ = 1 and A · A′ = 0

Question 9

What is the Double Negation/Involution Law in Boolean algebra?

Answer 9

(A′)′ = A

Question 10

What is the Commutative Law in Boolean algebra?

Answer 10

A + B = B + A and A · B = B · A

Question 11

What is the Associative Law in Boolean algebra?

Answer 11

(A + B) + C = A + (B + C) and (A · B) · C = A · (B · C)

Question 12

What is the Distributive Law in Boolean algebra?

Answer 12

A · (B + C) = A · B + A · C and A + (B · C) = (A + B) · (A + C)

Question 13

What does A + 0 simplify to in Boolean algebra?

Answer 13

A

Question 14

What does A · 1 simplify to in Boolean algebra?

Answer 14

A

Question 15

What does A + 1 simplify to in Boolean algebra?

Answer 15

1

Question 16

What does A · 0 simplify to in Boolean algebra?

Answer 16

0

Question 17

What does A + A simplify to in Boolean algebra?

Answer 17

A

Question 18

What does A · A simplify to in Boolean algebra?

Answer 18

A

Question 19

What does A + A′ simplify to?

Answer 19

1

Question 20

What does A · A′ simplify to?

Answer 20

0

Question 21

What is the result of double complement (A′)′?

Answer 21

A

Question 22

What does A + AB simplify to?

Answer 22

A

Question 23

What does A(A + B) simplify to?

Answer 23

A

Question 24

What does A + A′B simplify to?

Answer 24

A + B

Question 25

What is the first De Morgan's Theorem?

Answer 25

(A · B)′ = A′ + B′

Question 26

What is the second De Morgan's Theorem?

Answer 26

(A + B)′ = A′ · B′

Question 27

What is the complement of (A · B)?

Answer 27

A′ + B′

Question 28

What is the complement of (A + B)?

Answer 28

A′ · B′

Question 29

What is a Karnaugh Map (K-map)?

Answer 29

A Karnaugh Map is a graphical tool used to simplify Boolean expressions by organizing input combinations in a way that makes logical minimization easier.

Question 30

What are the applications of a Karnaugh Map?

Answer 30

K-maps are used for simplifying logic circuits, minimizing the number of logic gates, designing combinational logic, error detection and correction, optimizing programmable logic devices, and simplifying state tables in sequential circuits.

Question 31

What is De Morgan's Theorem?

Answer 31

De Morgan's Theorem provides rules for converting AND operations to OR operations and vice versa in complemented Boolean expressions: (A·B)' = A' + B' and (A + B)' = A'·B'.