How is each Gray bit obtained from binary?

XOR of two adjacent binary bits; MSB copied

2076 Chaitra · 1.5 marks

Convert (17)₁₀ to Gray

Short answer

17₁₀ = 10001₂. Gray code: keep MSB 1, then XOR each adjacent binary bit: 1⊕0=1, 0⊕0=0, 0⊕0=0, 0⊕1=1 → 11001 (Gray).

Convert (17)₁₀ = (?)gray.

First convert decimal to binary, then to Gray code: the MSB stays the same and each next Gray bit is the XOR of two adjacent binary bits, $G_i = B_{i+1} \oplus B_i$ .

Step 1: $17_{10} = 16 + 1 = (10001)_2$

Step 2: Binary to Gray

Binary bits	Operation	Gray bit
1	copy MSB	1
1, 0	$1 \oplus 0$	1
0, 0	$0 \oplus 0$	0
0, 0	$0 \oplus 0$	0
0, 1	$0 \oplus 1$	1

Answer: $(17)_{10} = (10001)_2 = (11001)_{gray}$

✓ Answer checked by Claude Opus 5.5 (high effort)

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