Gray code concept — evaluate the statement: “In Gray code, each number is 3 greater than the binary representation of that number.” Consider the defining property of Gray code (single-bit transitions) versus ordinary binary counting.

Introduction / Context:
Gray code (reflected binary code) is a binary numeral system where successive values differ by exactly one bit. It is used in position encoders, error reduction in A/D conversion, and state machines to minimize transition ambiguity. This question asks whether Gray code values are simply “3 greater than” ordinary binary numbers, which would imply a fixed arithmetic offset relationship between the two systems.

Given Data / Assumptions:

• Gray code is defined by single-bit adjacency, not arithmetic displacement.
• Binary numbers follow standard base-2 positional weighting (1, 2, 4, 8, ...).
• The statement proposes a fixed +3 mapping from binary to Gray.

Concept / Approach:
Converting binary to Gray involves bitwise operations: Gray MSB equals binary MSB; each subsequent Gray bit equals the XOR of adjacent binary bits (G_i = B_i XOR B_{i+1}). There is no constant arithmetic offset that globally maps binary to Gray or vice versa. The relationship is positional and bitwise, not additive.

Step-by-Step Solution:

Verification / Alternative check:
An inverse mapping exists but is cumulative XOR, not subtraction of a constant. Numerous tables show that Gray and binary sequences interleave, but do not differ by a uniform numeric offset.

Why Other Options Are Wrong:

• Correct / Only for even numbers / Only for 3-bit words: None fit because the mapping is never a constant +3 for any general subset.

Common Pitfalls:
Assuming a simple arithmetic formula connects all numeral systems; misunderstanding that Gray code is constructed for transition properties, not arithmetic convenience.

Final Answer:
Incorrect — Gray code is not obtained by adding 3 to binary; it uses bitwise rules to ensure single-bit transitions.