Question

Which 3-input gate outputs a false value only when all inputs are true?

a) AND
b) NAND
c) OR
d) NOR
e) XOR
f) XNOR

Answer 1

(b) NAND

(d) NOR

(f) XNOR

Step-by-step explanation:

This is best explained using a truth table.

A truth table containing 3 hypothetical inputs and their corresponding outputs using the AND, NAND, OR, NOR, XOR, and XNOR gates, has been attached to this response.

From the table, it can be seen that the NAND, NOR and XNOR gates produce a false value (0) when all inputs are true.

Note:

On the table,

For the AND column, a 1 is being output only when all three inputs are 1. Otherwise, a 0 results.

For the NAND column (which is the negation of the AND), a 0 is being output only when all three inputs are 0. Otherwise, a 1 results.

For the OR column, a 1 is being output when at least one of the three inputs is 1. Otherwise, a 0 results.

For the NOR column (which is the negation of the OR), a 0 is being output when at least one of the three inputs is 0. Otherwise, a 1 results.

For the XOR column, a 1 is being output when the number of inputs that are true (1) is odd. i.e when the number of 1s is 1 or 3. Otherwise, a 0 results.

For the XNOR column (which is the negation of the XOR), a 0 is being output when the number of inputs that are true (1) is odd. i.e when the number of 1s is 1 or 3. Otherwise, a 1 results.