What is the Gray bit rule for binary?

MSB copied; every other bit = binary bit XOR the bit to its left

2072 Chaitra · 2 marks

Convert (101001001)₂ to Gray

Short answer

MSB unchanged; each next Gray bit is XOR of current and previous binary bits. 101001001 binary gives 111101101 Gray.

Convert (101001001)binary = (?)Gray.

Rule: the MSB of the Gray code equals the MSB of binary; every other Gray bit is the XOR of the corresponding binary bit and the bit to its left: $G_i = B_{i+1} \oplus B_i$ .

Binary pair	XOR	Gray bit
MSB 1	copy	1
1, 0	1 ⊕ 0	1
0, 1	0 ⊕ 1	1
1, 0	1 ⊕ 0	1
0, 0	0 ⊕ 0	0
0, 1	0 ⊕ 1	1
1, 0	1 ⊕ 0	1
0, 0	0 ⊕ 0	0
0, 1	0 ⊕ 1	1

Answer: $(101001001)_2 = (111101101)_{Gray}$

✓ Answer checked by Claude Opus 5.5 (high effort)

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