How is each next binary bit found?

Previous Gray bit XOR current Gray bit

Previous binary bit AND current Gray bit

How can the result be checked?

Convert it back to Gray with G_i = B_(i+1) XOR B_i

2079 Bhadra · 1.5 marks

Convert (01010111)gray to binary

Short answer

MSB of binary equals MSB of Gray (0). Each next binary bit = previous binary bit XOR current Gray bit: 0⊕1=1, 1⊕0=1, 1⊕1=0, 0⊕0=0, 0⊕1=1, 1⊕1=0, 0⊕1=1. Result: (01100101)₂.

Convert (01010111)gray = (?)₂.

Rule (Gray to binary): the MSB of binary equals the MSB of Gray. Each next binary bit = previous binary bit XOR current Gray bit, $B_i = B_{i+1} \oplus G_i$ .

Gray bit $G_i$	Operation	Binary bit $B_i$
0	copy MSB	0
1	$0 \oplus 1$	1
0	$1 \oplus 0$	1
1	$1 \oplus 1$	0
0	$0 \oplus 0$	0
1	$0 \oplus 1$	1
1	$1 \oplus 1$	0
1	$0 \oplus 1$	1

Check: converting 01100101 back to Gray ( $G_i = B_{i+1} \oplus B_i$ ) gives 01010111 again.

Answer: $(01010111)_{gray} = (01100101)_2$ (= $101_{10}$ ).

✓ Answer checked by Claude Opus 5.5 (high effort)

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