Binary to Gray-code conversion Convert the 4-bit binary number 1100₂ to its equivalent Gray code.

Introduction / Context:Gray code changes only one bit between successive values, reducing errors in position encoders and asynchronous signal transfers. Converting between binary and Gray is a common interview and lab exercise.

Given Data / Assumptions:

• Binary input: 1100 (b3 b2 b1 b0).
• We want standard reflected binary Gray code.
• No arithmetic beyond XOR operations is required.

Concept / Approach:Rules for binary → Gray: g3 = b3; g2 = b3 XOR b2; g1 = b2 XOR b1; g0 = b1 XOR b0. Apply bitwise XORs from the binary input to produce the Gray output.

Step-by-Step Solution:

Verification / Alternative check:Reverse (Gray → Binary) to confirm: b3 = g3 = 1; b2 = b3 XOR g2 = 1 XOR 0 = 1; b1 = b2 XOR g1 = 1 XOR 1 = 0; b0 = b1 XOR g0 = 0 XOR 0 = 0 → 1100, matching the original.

Why Other Options Are Wrong:

• 0011, 1001, 1100: do not satisfy Gray-code conversion for 1100₂.

Common Pitfalls:Using XOR with the wrong neighbor bit or copying the binary number unchanged.

Final Answer:1010