What is the rule for Gray to binary conversion?

Copy MSB; each next binary bit = previous binary bit XOR current Gray bit

Each binary bit = Gray bit AND previous Gray bit

Each binary bit = XOR of adjacent Gray bits

(1110)gray→BCD and (1430)₁₀→Excess-3

Short answer

(i) Gray 1110 → binary 1011 (decimal 11) → BCD 0001 0001. (ii) Decimal 1430: add 3 to each digit → 4,7,6,3 → Excess-3 0100 0111 0110 0011.

Perform the following code conversions: i) (1110)gray = (?)BCD ii) (1430)₁₀ = (?)Excess-3

Step 1: Gray to binary. Copy the MSB; each next binary bit = previous binary bit ⊕ current Gray bit.

$(1110)_{Gray} = (1011)_2 = 8 + 2 + 1 = (11)_{10}$

Step 2: decimal to BCD. Code each digit: 1 → 0001, 1 → 0001.

Answer: $(1110)_{Gray} = (0001\ 0001)_{BCD}$

Add 3 to each digit and write it in 4 bits:

Answer: $(1430)_{10} = (0100\ 0111\ 0110\ 0011)_{XS-3}$

✓ Answer checked by Claude Opus 5.5 (high effort)