Q.Draw the NAND gate equivalent circuit of Half Subtractor.

A half subtractor computes A minus B, giving a difference and a borrow, and since NAND is a universal gate both outputs can be built from NAND gates only. …

[!TLDR]

A half subtractor's outputs, Difference $= A \oplus B$ and Borrow $= \overline{A}B$, are both realized using only 2-input NAND gates.

A half subtractor subtracts one bit B from another bit A. From its truth table the Difference is $D = A \oplus B$ (it is 1 whenever the two inputs differ) and the Borrow is $B_o = \overline{A}B$ (a borrow is required only when $A = 0$ and $B = 1$).

Because NAND is a universal gate, both outputs are produced with NAND gates alone. The XOR needed for the difference is the classic four-NAND network: Gate 1 forms $\overline{AB}$; Gate 2 forms $\overline{A\cdot\overline{AB}}$; Gate 3 forms $\overline{B\cdot\overline{AB}}$; and Gate 4 combines the Gate-2 and Gate-3 outputs as $\overline{\overline{A\cdot\overline{AB}}\cdot\overline{B\cdot\overline{AB}}} = A \oplus B$, which is the Difference …