Q.Convert the gray code 1000 into binary using XOR gates.

In gray-to-binary conversion the MSB is copied directly, and each remaining binary bit is the XOR of the previous binary bit with the current gray bit. Applying this to gray $1000$ gives binary $1111$ (decimal 15). …

[!TLDR]

Copy the MSB and XOR each previous binary bit with the next gray bit: gray $1000$ converts to binary $1111$.

The rule for gray-to-binary conversion using XOR gates is:

1. The most significant binary bit equals the most significant gray bit.
2. Every other binary bit is obtained by XOR-ing the immediately higher (already found) binary bit with the corresponding gray bit.

Let the gray input be $G_3 G_2 G_1 G_0 = 1000$ and the binary output be $B_3 B_2 B_1 B_0$:

• $B_3 = G_3 = 1$
• $B_2 = B_3 \oplus G_2 = 1 \oplus 0 = 1$
• $B_1 = B_2 \oplus G_1 = 1 \oplus 0 = 1$
• $B_0 = B_1 \oplus G_0 = 1 \oplus 0 = 1$ …