Q4. A two-input gate gives the outputs 1, 1, 1, 0 for the inputs 00, 01, 10, 11. Name the gate and write its Boolean expression.
A NAND gate: its output is 0 only when both inputs are 1, so Y is the complement of A·B (NEETS Module 13, page 2-14).
Q5. Show that a NOR gate with its two inputs joined together works as a NOT gate.
Both inputs are A, so the output is the complement of A + A. Since A + A = A (0 + 0 = 0, 1 + 1 = 1), the output is NOT A: 1 for A = 0 and 0 for A = 1.
Q6. The inputs A and B go to an OR gate, its output goes through a NOT gate, and that output and a third input C go to an AND gate. Write the final output and find it for A = 0, B = 0, C = 1.
Y = . For A = 0, B = 0, A + B = 0, so its complement is 1, and Y = 1·1 = 1.
Q7. Assertion: the NAND gate is called a universal gate. Reason: NOT, AND and OR gates can all be made from NAND gates alone. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (Wikipedia, “Logic gate”; see the NAND and NOR gates section).
Q8. In positive logic, which of two voltage levels stands for the logic 1 state?
The more positive one, called HIGH; the less positive level, LOW, stands for 0 (NEETS Module 13, page 2-3).
Q9. Two inputs go to an AND gate whose output is inverted by a NOT gate. Which single gate could replace the pair, and what is its output for A = 1, B = 1?
A NAND gate, which is an AND gate followed by a NOT gate. For A = 1, B = 1 the AND gives 1, so the output is 0.