1.4.3 - Boolean Algebra

Question 1

What is Boolean algebra?

Answer 1

A branch of algebra where variables represent true (1) or false (0) values.

Question 2

What are the four basic Boolean operations?

Answer 2

Conjunction (AND), Disjunction (OR), Negation (NOT), Exclusive Disjunction (XOR).

Question 3

What is the symbol for the AND operation?

Answer 3

∧

Question 4

What is the truth table for an AND gate?

Answer 4

Output is 1 only if both inputs are 1.

Question 5

What is the symbol for the OR operation?

Answer 5

∨

Question 6

What is the truth table for an OR gate?

Answer 6

Output is 1 if at least one input is 1.

Question 7

What is the symbol for the NOT operation?

Answer 7

¬

Question 8

What is the truth table for a NOT gate?

Answer 8

Output is the inverse of the input.

Question 9

What is the symbol for the XOR operation?

Answer 9

⊕ or ∨ with a line underneath (context dependent).

Question 10

What is the truth table for an XOR gate?

Answer 10

Output is 1 only if the inputs are different.

Question 11

What is a truth table?

Answer 11

A table showing all possible input combinations and their corresponding outputs for a logic expression.

Question 12

What is the purpose of a Karnaugh map (K-map)?

Answer 12

To simplify Boolean expressions visually.

Question 13

What is a key feature of the row/column labels in a K-map?

Answer 13

They use Gray code, where adjacent cells differ by only one bit.

Question 14

What is the main goal when grouping ‘1’s in a K-map?

Answer 14

To create the largest possible groups (sizes that are powers of 2) to simplify the expression.

Question 15

What are De Morgan’s Laws?

Answer 15

¬(A ∧ B) ≡ ¬A ∨ ¬B and ¬(A ∨ B) ≡ ¬A ∧ ¬B

Question 16

What is the Distributive Law in Boolean algebra?

Answer 16

A ∧ (B ∨ C) ≡ (A ∧ B) ∨ (A ∧ C) and A ∨ (B ∧ C) ≡ (A ∨ B) ∧ (A ∨ C)

Question 17

What is the Associative Law in Boolean algebra?

Answer 17

(A ∧ B) ∧ C ≡ A ∧ (B ∧ C) and (A ∨ B) ∨ C ≡ A ∨ (B ∨ C)

Question 18

What is the Commutative Law in Boolean algebra?

Answer 18

A ∧ B ≡ B ∧ A and A ∨ B ≡ B ∨ A

Question 19

What is the Law of Double Negation?

Answer 19

¬(¬A) ≡ A

Question 20

What is a D-type flip-flop?

Answer 20

A logic circuit that can store one bit of data, updating its output (Q) to match its input (D) on the rising edge of a clock signal.

Question 21

What is the primary function of a flip-flop?

Answer 21

To act as a basic memory unit (1-bit storage).

Question 22

What is a half adder?

Answer 22

A circuit that adds two single-bit inputs (A and B) and produces a sum (S) and a carry (C) output.

Question 23

What logic gates make up a half adder?

Answer 23

An XOR gate for the sum and an AND gate for the carry.

Question 24

What is the truth table for a half adder?

Answer 24

A=0,B=0 -> S=0,C=0; A=0,B=1 -> S=1,C=0; A=1,B=0 -> S=1,C=0; A=1,B=1 -> S=0,C=1

Question 25

What is a full adder?

Answer 25

A circuit that adds three single-bit inputs (A, B, and Carry-in) and produces a sum and a carry-out output.

Question 26

What logic gates make up a full adder?

Answer 26

Typically two XOR gates, two AND gates, and one OR gate.

Question 27

What is the main advantage of a full adder over a half adder?

Answer 27

It can handle a carry-in from a previous addition, allowing multiple adders to be chained.

Question 28

What is a ripple carry adder?

Answer 28

Multiple full adders connected in series, where the carry-out from one adder is fed into the carry-in of the next.

Question 29

How many rows are in a full adder's truth table?

Answer 29

8 rows (for 3 inputs).

Question 30

What is the output of a Boolean expression?

Answer 30

Either True (1) or False (0).

Question 31

What is the purpose of simplifying a Boolean expression?

Answer 31

To create a logically equivalent but simpler circuit, reducing cost and complexity.