Logic Gates & Boolean Algebra

Question 1

What are logic gates, and why are they important?

Answer 1

Logic gates perform basic logical functions and are the fundamental building blocks of digital circuits. Examples include AND, OR, NOT, NAND, NOR, and XOR.

Question 2

What is the symbol and Boolean equation for a NOT gate?

Answer 2

Symbol: Inverted triangle with a circle.
Boolean equation:
A
‾
A
.

Question 3

What is the truth table for an AND gate?

Answer 3

A B A ∙ B
0 0 0
0 1 0
1 0 0
1 1 1

Question 4

What are the types of logic gates and their functions?

Answer 4

AND: Outputs 1 only if all inputs are 1.
OR: Outputs 1 if any input is 1.
NOT: Inverts the input.
NAND: Outputs 0 only if all inputs are 1.
NOR: Outputs 1 only if all inputs are 0.
XOR: Outputs 1 if inputs are different.

Question 5

What is the identity for A.1

Answer 5

A⋅1=A.

Question 6

What is the identity for A+0?

Answer 6

A+0=A.

Question 7

What does DeMorgan’s Theorem state?

Answer 7

—- — —
A.B=A +B
—— — —
A+B=A.B

Question 8

What is the purpose of Boolean algebra?

Answer 8

To simplify logic expressions by removing redundancies and using identities for minimal circuit design.

Question 9

How do you derive Boolean expressions from a logic circuit?

Answer 9

Start from the inputs, work across the circuit to the outputs, and identify stages to write Boolean equations for each stage.

Question 10

What is a half adder?

Answer 10

A circuit that adds two bits and outputs a sum and carry.

Question 11

What is the difference between a half adder and a full adder?

Answer 11

A full adder adds three inputs (A, B, and Carry-in) and outputs a sum and carry-out, while a half adder adds only two inputs (A and B).

Question 12

What is the purpose of a D-type flip-flop?

Answer 12

To store a single bit of data (0 or 1).

Question 13

What are the inputs and outputs of a D-type flip-flop?

Answer 13

Inputs: Data (D) and Clock.
Outputs:
Q (stored bit) and Q’(complement of Q).

Question 14

How can a D-type flip-flop be used in a burglar alarm system?

Answer 14

It can store the alarm state, ensuring the alarm remains active even if triggering conditions change (e.g., door closes or weight is removed).

Question 15

_
Simplify A.(B+NotB)

Answer 15

A.1=A

Question 16

Draw the circuit for
Q=(A+B)⋅C

Answer 16

Use an OR gate for
A
+
B
A+B, followed by an AND gate with input
C
C.

Question 17

What is the truth table for a full adder?

Answer 17

A B Cin Sum Cout
0 0 0 0 0
0 1 0 1 0
1 0 0 1 0
1 1 0 0 1
0 0 1 1 0
0 1 1 0 1
1 0 1 0 1
1 1 1 1 1