GATE CS 2006 Q40 — Number Representations (Fixed and Floating Point)

To find the correct function, we map each decimal value $n \in [0, 15]$ to its 4-bit Gray code representation $H(n) = h_3h_2h_1h_0$. The decimal value of this Gray code (interpreted as a standard binary number) represents the minterm index $D$. We then find the Gray code of $(n+1) \pmod{16}$, which is $G(n) = g_3g_2g_1g_0$.

The mapping table for all 16 values is as follows:

Now, we collect the minterm indices $D$ where each output bit $g_i$ is $1$:

• For $g_2$, the bit is $1$ at $D \in \{2, 4, 5, 6, 7, 12, 13, 15\}$.

This matches Option C: $g_{2}(h_{3}h_{2}h_{1}h_{0})=\sum (2, 4, 5, 6, 7, 12, 13, 15)$.