In which of the following gates, the output is high if and only if all inputs are high?

Question

Prepp Team · Accepted Answer

Logic gates are fundamental building blocks of digital electronic circuits. They perform basic logical operations on one or more binary inputs and produce a single binary output. The output of a logic gate is typically represented as 'high' (often representing a 1 or true) or 'low' (often representing a 0 or false).

AND Gate Functionality

The AND gate is a type of logic gate where the output is high (or TRUE) if and only if all of its inputs are high (or TRUE). If any one of the inputs is low (or FALSE), then the output will be low (or FALSE). This behavior perfectly matches the description given in the question: "the output is high if and only if all inputs are high".

Let's consider a simple AND gate with two inputs, A and B, and an output Y.

AND Gate Truth Table
Input A	Input B	Output Y = A & B
0 (Low)	0 (Low)	0 (Low)
0 (Low)	1 (High)	0 (Low)
1 (High)	0 (Low)	0 (Low)
1 (High)	1 (High)	1 (High)

As you can see from the AND gate truth table, the output Y is 1 (high) only when both input A and input B are 1 (high). This confirms the AND gate's property of providing a high output exclusively when all its inputs are high.

NOT Gate Behavior

The NOT gate, also known as an inverter, is a single-input logic gate. Its output is always the complement or inverse of its input. If the input is high, the output is low, and if the input is low, the output is high. It does not require all inputs to be high to produce a high output, as it only has one input, and its output is high only if that single input is low.

NOT Gate Truth Table
Input A	Output Y = $\overline{A}$
0 (Low)	1 (High)
1 (High)	0 (Low)

Therefore, the NOT gate does not fit the description where the output is high if and only if all inputs are high.

XOR Gate Characteristics

The XOR gate (Exclusive OR) is a logic gate whose output is high (TRUE) if an odd number of inputs are high (TRUE). For a two-input XOR gate, the output is high if either input A is high or input B is high, but not if both are high or both are low. This is different from the condition "all inputs are high".

XOR Gate Truth Table
Input A	Input B	Output Y = A $\oplus$ B
0 (Low)	0 (Low)	0 (Low)
0 (Low)	1 (High)	1 (High)
1 (High)	0 (Low)	1 (High)
1 (High)	1 (High)	0 (Low)

As shown in the XOR gate truth table, when both inputs are high (A=1, B=1), the output Y is low (0). This contradicts the requirement that the output must be high when all inputs are high.

OR Gate Principles

The OR gate is a logic gate where the output is high (TRUE) if at least one of its inputs is high (TRUE). The output is low (FALSE) only when all inputs are low (FALSE). This means that if input A is high, or input B is high, or both A and B are high, the output will be high.

OR Gate Truth Table
Input A	Input B	Output Y = A + B
0 (Low)	0 (Low)	0 (Low)
0 (Low)	1 (High)	1 (High)
1 (High)	0 (Low)	1 (High)
1 (High)	1 (High)	1 (High)

While the OR gate output is high when all inputs are high (last row of the truth table), it is also high when only one input is high (second and third rows). The question specifies "if and only if all inputs are high," which means this is the only condition for a high output. The OR gate does not meet this exclusivity criterion.

Logic Gate Output Summary

Comparing the behavior of all discussed logic gates against the condition "the output is high if and only if all inputs are high":

NOT Gate: Output is high when input is low. (Does not fit)
XOR Gate: Output is high when inputs are different, low when all inputs are high. (Does not fit)
OR Gate: Output is high if at least one input is high. (Does not fit the "if and only if" condition)
AND Gate: Output is high exclusively when all inputs are high. (Fits perfectly)

Therefore, the AND gate is the logic gate where the output is high if and only if all its inputs are high.