NIMCET 2008 — Computer PYQ

Step 1: Simplify the complemented term

Let’s focus on the second part of the expression: $P=\overline{(\bar{z}+x+y)(\bar{x}+\bar{y})}$.

Using De Morgan's Law ($\overline{A\cdot B}=\bar{A}+\bar{B}$):

Now apply De Morgan's Law again to the individual parts ($\overline{A+B+C}=\bar{A}\bar{B}\bar{C}$):

1. $\overline{(\bar{z}+x+y)}=z\bar{x}\bar{y}$

2. $\overline{(\bar{x}+\bar{y})}=xy$

So, the second part $P$ becomes:

Step 2: Combine with the first part of the function

Now substitute $P$ back into the original function $f(x,y,z)$:

Step 3: Factor and simplify

Group the terms involving $z$:

Using the identity $(x+y+\bar{x}\bar{y})=(x+y+\overline{x+y})$. We know that $A+\bar{A}=1$. Here $A=(x+y)$.

Therefore:

The expression simplifies to:

Step 4: Count the gates

The simplified function is $f=z+xy$.

To implement this:

1. One AND gate is needed for the product $xy$.

2. One OR gate is needed to add $z$ to the result of $xy$.

Total number of gates = 2.

Final Answer:

The correct option is (a) 2.