Bit Manipulation - Gray Code
Given the Gray code sequence output for n=3:
[0, 1, 3, 2, 6, 7, 5, 4]
Which original binary number corresponds to the Gray code 5 in this sequence?
Given the Gray code sequence output for n=3: [0, 1, 3, 2, 6, 7, 5, 4] Which original binary number corresponds to the Gray code 5 in this sequence?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Recall Gray code to binary conversion
Binary = Gray ^ (Gray >> 1) ^ (Gray >> 2) ... until shift is 0.Step 2: Convert Gray code 5 (binary 101) back to binary
5 ^ (5 >> 1) = 5 ^ 2 = 7; further shifts do not change the result.Final Answer:
Option A -> Option AQuick Check:
Gray code 5 corresponds to binary 7 [OK]
Quick Trick: Invert Gray code by iterative XOR with shifted versions [OK]
Common Mistakes:
MISTAKES- Confusing Gray code with binary directly
- Incorrect bitwise inversion
Trap Explanation:
PITFALL- Candidates often forget how to invert Gray code to original binary number.
Interviewer Note:
CONTEXT- Tests deep understanding of Gray code encoding and decoding.
Master "Gray Code" in Bit Manipulation
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