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 X and Y and output Z. Fill in the table headers and all missing values. Inputs: X, Y Output: Z

Answer: Truth table: X | Y | Z 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1

Question 3: Draw the logic circuit for a circuit with an AND gate, a NOT gate, and an OR gate arranged so that the output is high only when either both inputs are high or the first input is low.

Answer: A correct circuit would include: two inputs feeding into an AND gate and a NOT gate (taking the first input), then an OR gate combining the outputs of the AND gate and the NOT gate. The final output comes from the OR gate.

Question 4: Express the Boolean expression (A AND B) OR (A AND C) in simplified form using Boolean algebra rules.

Answer: The expression simplifies to A AND (B OR C).

Question 5: Describe verbally what the output of an XOR gate would be if both inputs are high (1).

Answer: The output would be low (0) because XOR outputs true only when inputs are different.

Question 6: Sketch a truth table for the NOR gate with inputs P and Q. Include all possible input combinations and the corresponding output.

Answer: Truth table: P | Q | Output 0 | 0 | 1 0 | 1 | 0 1 | 0 | 0 1 | 1 | 0

Question 7: Complete the Boolean algebra law: A OR (A AND B) = ?

Answer: The expression simplifies to A, according to the absorption law.

Question 8: Draw a logic circuit that uses only NAND gates to implement an AND function.

Answer: A correct circuit involves: two NAND gates. The first NAND gate takes inputs A and B; the output is then fed into both inputs of a second NAND gate, which produces the AND function.

Question 9: Explain why the NOT gate is used in a circuit that needs to invert a signal.

Answer: The NOT gate outputs the opposite value of its input, so it is used to invert the signal when a logical 'not' is required.

Question 10: Write the Boolean expression for a circuit with three inputs A, B, and C, where the output is true only when exactly two inputs are true.

Answer: The expression is (A AND B AND NOT C) OR (A AND NOT B AND C) OR (NOT A AND B AND C).

Question 11: Describe in words what happens when both inputs to an XOR gate are different.

Answer: The XOR gate outputs a high signal (1) when the inputs are different.