ITPEC FE Subject B April 2025 Question 6

Gray Code to Binary Conversion — fill in bitwise operations for iterative Gray-to-binary decoding.

The standard algorithm converts Gray code to binary by XOR-accumulating shifted copies of the input:

1. Start with y = x and z = x
2. In each iteration: shift z right by 1, then XOR y with z
3. Stop when z becomes 00000000

This works because each binary bit equals the XOR of all Gray code bits from the MSB down to that position. The right-shift progressively brings higher bits into alignment for XOR.

Verification with GrayBiCon(00001100):

Result: 00001000 — matches the expected output.

Why not others:
- (a–c) use & (AND) for blank A — AND removes bits rather than shifting them; the algorithm needs to progressively shift z rightward
- (d–f) use << (left shift) for blank A — shifting left moves bits toward MSB, but the algorithm must scan from MSB to LSB
- (g) uses >> + y & z — AND masks bits instead of XOR-accumulating them
- (i) uses >> + y | z — OR sets bits but never clears them, producing incorrect results

Key rule: Gray-to-binary conversion uses y ^= (y >> n) pattern — right-shift to propagate MSB influence downward, XOR to accumulate.

AI-generated — may contain errors