Introduction
To implement a half subtractor using NOR gates, we need to understand the basic concept of a half subtractor and the logic behind its implementation using NOR gates.

Half Subtractor
A half subtractor is a combinational logic circuit that performs the subtraction of two single-bit numbers. It has two inputs: the minuend (A) and the subtrahend (B). The half subtractor produces two outputs: the difference (D) and the borrow (Bout).

Truth Table of a Half Subtractor
The truth table of a half subtractor is as follows:

Inputs Outputs
A B D Bout
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

Implementation using NOR gates
To implement a half subtractor using NOR gates, we can use the following logic:

1. Implementing the difference (D):
- The difference (D) can be obtained by connecting both inputs (A and B) to a NOR gate.

2. Implementing the borrow (Bout):
- The borrow (Bout) can be obtained by connecting the inputs (A and B) to a NOR gate, and then connecting the output of this NOR gate to another NOR gate with input A.

Calculating the minimum number of NOR gates
To calculate the minimum number of NOR gates required, we need to analyze the logic expression and simplify it using Boolean algebra.

1. Simplifying the difference (D) logic expression:
- The logic expression for D is D = A NOR B.
- This requires one NOR gate.

2. Simplifying the borrow (Bout) logic expression:
- The logic expression for Bout is Bout = (A NOR B) NOR A.
- This requires two NOR gates.

Therefore, the minimum number of NOR gates needed to implement a half subtractor is 1 NOR gate for the difference and 2 NOR gates for the borrow, totaling 3 NOR gates.

However, the given correct answer is '5'. To achieve this, we need to consider the implementation of a half subtractor using only 2-input NOR gates. In this case, we can break down the logic expressions further:

1. Simplifying the difference (D) logic expression:
- The logic expression for D is D = A NOR B.
- This requires one NOR gate.

2. Simplifying the borrow (Bout) logic expression:
- The logic expression for Bout is Bout = (A NOR B) NOR (A NOR B).
- This requires three NOR gates.

Therefore, the minimum number of 2-input NOR gates needed to implement a half subtractor is 1 NOR gate for the difference and 3 NOR gates for the borrow, totaling 4 NOR gates. However, since the question specifies a minimum of 5 NOR gates, it may involve additional constraints or specific circuit configurations not mentioned in the given information.