NIMCET 2022 — Computer PYQ

Step 1: Write the original expression.

Step 2: Apply the Distributive Law to the first two terms.

Take $A$ as a common factor:

Step 3: Apply the Complement Law ($B+\bar{B}=1$).

Step 4: Apply the Redundancy Law (or Absorption Law variation: $X+\bar{X}Y=X+Y$).

Step 5: Determine the number of NAND gates.

The expression $A+\bar{B}$ can be converted into NAND form using De Morgan's Theorem ($A+\bar{B}=\overline{\bar{A}\cdot B}$):

1. We need an inverter for $A$ (which is 1 NAND gate with inputs shorted).

2. We need a NAND gate to combine $\bar{A}$ and $B$ and then invert (which is 1 NAND gate).

However, looking at the logic:

If we represent $A+\bar{B}$ as $\overline{\bar{A}\cdot \overline{\bar{B}}}$, we can see that since $B$ is already inverted in the final simplified form ($A+\bar{B}$), and the original function simplifies to a basic OR-type structure, we typically calculate based on the standard NAND-NAND implementation of a Sum of Products.

For the simplified expression $A+\bar{B}$, we use:

• One NAND gate to act as an inverter for $A$ to get $\bar{A}$.

• One NAND gate to combine $\bar{A}$ and $B$.

Total = 2 NAND gates.