Gray-to-binary conversion Convert the 4-bit Gray code 1011 to standard binary.

Introduction / Context:
Gray code is a binary numeral system where adjacent values differ by only one bit. Converting Gray to binary is a common digital logic task, often needed for encoders and error minimization.

Given Data / Assumptions:

• Gray code bits (g3 g2 g1 g0) = 1 0 1 1.
• Binary bits (b3 b2 b1 b0) are computed iteratively.
• Rule: b3 = g3; then b(n) = b(n+1) XOR g(n) as you move toward LSB.

Concept / Approach:
Start with the MSB unchanged, then XOR each subsequent Gray bit with the previous binary bit to obtain the next binary bit.

Step-by-Step Solution:

Verification / Alternative check:
Convert back: Gray from 1101 → g3 = 1; g2 = b3 XOR b2 = 1 XOR 1 = 0; g1 = b2 XOR b1 = 1 XOR 0 = 1; g0 = b1 XOR b0 = 0 XOR 1 = 1 → 1011.

Why Other Options Are Wrong:

• 1011/1010/0100: Do not match the correct Gray-to-binary conversion result for 1011.

Common Pitfalls:
Using XOR with the next Gray bit instead of the previous binary bit, or starting from the LSB instead of the MSB.

Final Answer:
1101