Question 1: Simplify the Boolean expression: A AND (A OR B).

Answer: The simplified expression is A.

Question 2: Complete the truth table for the AND gate with inputs A and B. Fill in the output column.

Answer: When A=0, B=0, Output=0; When A=0, B=1, Output=0; When A=1, B=0, Output=0; When A=1, B=1, Output=1.

Question 3: Draw the logic circuit that represents the following Boolean expression: (A AND B) OR C.

Answer: A correct sketch would include two AND gates: one with inputs A and B, and the other with input C, with their outputs connected to an OR gate.

Question 4: Explain the difference between the logic gates AND, OR, and NOT in terms of their function.

Answer: The AND gate outputs 1 only when both inputs are 1; the OR gate outputs 1 when at least one input is 1; the NOT gate inverts the input, outputting 1 when input is 0 and vice versa.

Question 5: Complete the truth table for the OR gate with inputs A and B.

Answer: A=0, B=0, Output=0; A=0, B=1, Output=1; A=1, B=0, Output=1; A=1, B=1, Output=1.

Question 6: Sketch a logic circuit that implements the Boolean expression: NOT (A AND B).

Answer: A correct sketch would include an AND gate with inputs A and B, followed by a NOT gate (inverter) connected to the output of the AND gate.

Question 7: Describe what a NAND gate does and how it differs from an AND gate.

Answer: A NAND gate outputs 0 only when both inputs are 1; otherwise, it outputs 1. It is the inverse of an AND gate.

Question 8: Draw a truth table for the XOR (exclusive OR) gate with inputs A and B.

Answer: A=0, B=0, Output=0; A=0, B=1, Output=1; A=1, B=0, Output=1; A=1, B=1, Output=0.

Question 9: Explain why Boolean algebra is useful in designing digital circuits.

Answer: Boolean algebra allows for the simplification of logic expressions, making digital circuits more efficient, cost-effective, and easier to design and troubleshoot.

Question 10: Sketch a logic circuit that uses NOT, AND, and OR gates to implement the expression: (A OR B) AND (NOT C).

Answer: A correct sketch includes an OR gate with inputs A and B, a NOT gate for input C, and an AND gate that takes the outputs of these two gates.