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

In a half subtractor, the primary logical operations needed to find the difference between two binary inputs, typically denoted as $A$ and $B$, are:

1. XOR Operation: This operation is used to compute the difference. The output $D$ for the difference is given by: $D = A \oplus B$ where $\oplus$ represents the XOR (exclusive OR) operation.

2. AND Operation: To determine if there is a need to borrow, the half subtractor also utilizes an AND operation. The borrow output $B_{out}$ is computed as: $B_{out} = \overline{A} \cdot B$ where $\overline{A}$ is the NOT operation applied to input $A$, and $\cdot$ represents the AND operation.

Thus, to conclude, a half subtractor requires both the XOR and AND logical operations to compute the difference and the borrow, respectively.