How is Gray converted to decimal?

Convert to binary first, then to decimal

Add weights of the Gray bits directly

2080 Bhadra · 1.5 marks

Convert (10101)gray to decimal

Short answer

Convert Gray to binary by copying the MSB and XORing each successive bit: 1,1⊕0=1, 1⊕1=0, 0⊕0=0, 0⊕1=1 gives 11001₂. Decimal value is 16+8+1=25, so (25)₁₀.

Convert (10101)gray = (?)₁₀.

Gray to binary: copy the MSB; each next binary bit = previous binary bit ⊕ current Gray bit.

$B = 1,\ 1\oplus0 = 1,\ 1\oplus1 = 0,\ 0\oplus0 = 0,\ 0\oplus1 = 1$ → $(11001)_2$

$(11001)_2 = 16 + 8 + 1 = 25$

Answer: $(10101)_{Gray} = (25)_{10}$

✓ Answer checked by Claude Opus 5.5 (high effort)

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