In digital logic design using NAND gates, which of the following options correctly describes valid ways to convert a two input NAND gate into a simple inverter or NOT gate?

Introduction / Context:
NAND gates are universal gates, meaning they can be combined to implement any logical function, including NOT, AND, and OR. This question asks about specific wiring techniques that allow a two input NAND gate to act as a simple inverter. Understanding how to derive basic logic functions from universal gates is fundamental in digital logic design and integrated circuit implementation.

Given Data / Assumptions:

- We have a two input NAND gate with inputs A and B and output Y.- We want the gate to behave like an inverter, so Y should be the logical NOT of a single variable.- The options describe various ways of fixing or tying inputs to logic levels or to each other.

Concept / Approach:
The logical function of a two input NAND gate is Y = NOT(A * B). To make this behave like an inverter for a single variable X, we can either make both inputs equal to X, or we can fix one of the inputs to logic 1 and let the other input be X. In the first case, Y = NOT(X * X) = NOT(X). In the second case, Y = NOT(X * 1) = NOT(X). Any wiring that fixes inputs to logic 0 or grounds the output does not produce a proper inverting function for a changing data signal.

Step-by-Step Solution:
Step 1: Consider method one, where both inputs are tied together to a single signal X. Then the NAND gate computes Y = NOT(X * X).Step 2: Since X * X is equal to X in Boolean algebra, Y becomes NOT(X), which is exactly the behaviour of an inverter.Step 3: Consider method two, where input A is tied to logic 1 and input B is the signal X. The NAND gate computes Y = NOT(1 * X).Step 4: Because 1 * X equals X, again Y = NOT(X), so the NAND gate behaves as an inverter for X.Step 5: Option A explicitly describes both of these valid methods.Step 6: Option B ties both inputs to logic 0, which produces Y = NOT(0 * 0) = NOT(0) = 1, a constant output rather than an inverter.Step 7: Options C, D, and E describe configurations that either leave inputs floating or fix outputs, none of which provide a proper NOT function for a data signal.

Verification / Alternative check:
Truth table analysis confirms these conclusions. For the configuration with both inputs tied together, when X is 0, the output is 1; when X is 1, the output is 0. This matches the inverter truth table. For the configuration with one input at 1 and the other as X, the truth table also matches that of a NOT gate. Digital logic textbooks often show these wiring methods when teaching how to implement basic gates from NAND gates, which confirms that option A is correct.

Why Other Options Are Wrong:
Option B produces a constant 1 output, which does not depend on any input variable, so it is not an inverter. Option C leaves an input unconnected, which is bad practice and results in undefined behaviour. Option D uses two NAND gates in series without any fixed inputs, which normally results in more complex logic rather than a simple NOT. Option E forces the output to ground, producing a constant 0, again not an inverting function.

Common Pitfalls:
A common mistake is to think that tying inputs to 0 or grounding outputs is a valid way to create logic functions, but this usually results in fixed logic levels instead of useful gates. Another pitfall is to forget that Boolean algebra identities, such as X * X = X and 1 * X = X, are essential when reasoning about how gate configurations behave. Practicing with truth tables for different wiring schemes can help avoid such errors.

Final Answer:
The valid methods are to connect both inputs together to the same signal or tie one input to logic 1 and use the other as the data signal, as described in option A.