Which of the following gates has output LOW if and only if all the inputs are HIGH?

Question

Prepp Team · Accepted Answer

Logic Gate Analysis

Understanding the behavior of different logic gates is fundamental in digital electronics. Each logic gate performs a specific Boolean operation on its input signals to produce a single output signal. The question asks to identify the gate whose output is LOW if and only if all its inputs are HIGH.

NAND Gate Behavior

The NAND gate is a combination of an AND gate followed by a NOT gate (inverter). This means its output is the inverse of an AND gate's output.

An AND gate produces a HIGH output only when all its inputs are HIGH.
Therefore, a NAND gate produces a LOW output only when all its inputs are HIGH.
For all other combinations of inputs (where at least one input is LOW), the NAND gate's output will be HIGH.

Let's examine the truth table for a 2-input NAND gate:

$$\begin{array}{|c|c|c|} \hline \textbf{Input A} & \textbf{Input B} & \textbf{Output (A NAND B)} \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \hline \end{array}$$

As observed from the truth table, the output is 0 (LOW) only when both inputs A and B are 1 (HIGH). This perfectly matches the condition given in the question.

Other Gate Comparisons

Let's briefly look at the characteristics of the other options to understand why they do not fit the description.

NOR Gate Behavior

A NOR gate is a combination of an OR gate followed by a NOT gate. Its output is HIGH only when all its inputs are LOW. If any input is HIGH, the output will be LOW.

$$\begin{array}{|c|c|c|} \hline \textbf{Input A} & \textbf{Input B} & \textbf{Output (A NOR B)} \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 0 \\ \hline \end{array}$$

This does not match the condition "output LOW if and only if all the inputs are HIGH."

XOR Gate Behavior

An XOR (Exclusive OR) gate produces a HIGH output if an odd number of inputs are HIGH. For a 2-input XOR gate, the output is HIGH if the inputs are different, and LOW if they are the same.

$$\begin{array}{|c|c|c|} \hline \textbf{Input A} & \textbf{Input B} & \textbf{Output (A XOR B)} \\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \hline \end{array}$$

While its output is LOW when both inputs are HIGH, it is also LOW when both inputs are LOW. The condition in the question specifies "if and only if all the inputs are HIGH," which implies that this is the *only* condition for a LOW output. Therefore, XOR does not fit.

AND Gate Behavior

An AND gate produces a HIGH output if and only if all its inputs are HIGH. For all other input combinations, the output is LOW.

$$\begin{array}{|c|c|c|} \hline \textbf{Input A} & \textbf{Input B} & \textbf{Output (A AND B)} \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array}$$

This gate's output is HIGH when all inputs are HIGH, which is the opposite of the condition stated in the question (output LOW).

Conclusion on Logic Gates

Based on the analysis of the truth tables and definitions:

The NAND gate is the only logic gate among the given options whose output is LOW exclusively when all of its inputs are HIGH.
This characteristic makes the NAND gate a "universal" gate, meaning any other logic gate (AND, OR, NOT, NOR, XOR, XNOR) can be constructed using only NAND gates.