NIMCET 2010 — Computer PYQ

Solution

To simplify the given function $F(X,Y,Z)$, we use a 3-variable Karnaugh Map (K-Map). The minterms provided are $\{0,2,4,5,6\}$.

1. Map the Minterms:

• $m_0=\bar{X}\bar{Y}\bar{Z}$ (Binary 000)

• $m_2=\bar{X}Y\bar{Z}$ (Binary 010)

• $m_4=X\bar{Y}\bar{Z}$ (Binary 100)

• $m_5=X\bar{Y}Z$ (Binary 101)

• $m_6=XY\bar{Z}$ (Binary 110)

2. Form Groups:

• Quad (Group of 4): Looking at the corners and edges, we can group cells $m_0,m_2,m_4,$ and $m_6$. These four cells all have $Z=0$ in common.

  • Simplified term for this quad: $\bar{Z}$

• Pair (Group of 2): We still need to cover $m_5$. We can pair $m_5$ with $m_4$. In this pair, $X=1$ and $Y=0$ remain constant, while $Z$ changes.

  • Simplified term for this pair: $X\bar{Y}$

3. Combine the Results:

By summing the simplified terms from each group, we get the final Boolean expression:

Correct Answer:

The correct option is (b).