For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical expressions for the outputs $\text{D}$ ( = $\text{A}$ minus $\text{B}$ ) and $\text{X}(=$ borrow) are
- $\mathrm{D}=\mathrm{AB}+\overline{\mathrm{A}} \mathrm{B}, \mathrm{X}=\bar{A} \mathrm{~B}$
- $\mathrm{D}=\overline{\mathrm{A}} \mathrm{B}+\mathrm{A} \overline{\mathrm{B}}+\mathrm{A} \overline{\mathrm{B}}, X=\mathrm{A} \overline{\mathrm{B}}$
- $\mathrm{D}=\overline{\mathrm{A}} \mathrm{B}+\mathrm{A} \overline{\mathrm{B}}, \mathrm{X}=\bar{A} \mathrm{~B}$
- $\mathrm{D}=\mathrm{AB}+\overline{\mathrm{A}} \overline{\mathrm{B}}, \mathrm{X}=\mathrm{A} \overline{\mathrm{B}}$