Which of the following logical operation need to perform between two input  to find out the difference in a half subtractor ?EXORNORNANDOR

To determine the logical operations needed for a half subtractor, let's first understand what a half subtractor does. A half subtractor is a digital circuit used to subtract one binary digit (bit) from another. It takes two inputs, typically denoted as $A$ (the minuend) and $B$ (the subtrahend), and produces two outputs: the difference $D$ and the borrow $B_{out}$.

Step 1: Identify the Outputs

• Difference (D): This output can be derived using the XOR (exclusive OR) operation. The difference is high (1) when exactly one of the inputs is high.
• Borrow (B_out): This output indicates if a borrow is needed, which can be calculated using the operation $NOT\, A \, AND\, B$ or simply using the relation that if $A < B$, then a borrow occurs.

Step 2: Relevant Operations

• The difference $D$ can be represented as: $D = A \oplus B$ where $\oplus$ denotes the XOR operation.
• The borrow output $B_{out}$ can be represented as: $B_{out} = \overline{A} \cdot B$ where $\overline{A}$ is the NOT operation applied to $A$ and $\cdot$ denotes the AND operation.

Step 3: Verify and Summarize

The logical operations needed for the half subtractor are:

1. XOR operation for the difference.
2. AND operation with a NOT gate for the borrow.

Final Answer

The logical operation needed to find the difference in a half subtractor is XOR.