Gray code vs. Excess-3 — conceptual check Evaluate the statement: “In Gray code, each number is 3 greater than the binary representation of that number.”

Introduction / Context:
Gray code and Excess-3 are distinct numbering schemes used for different purposes. Gray code minimizes bit changes between adjacent values, while Excess-3 is a decimal code that offsets each BCD digit by +3 to simplify certain arithmetic processes and display logic. Mixing these definitions leads to common misconceptions on exams.

Given Data / Assumptions:

• Statement claims: Gray code equals binary + 3.
• Gray code property: single-bit change between successive values.
• Excess-3 property: each BCD digit = binary of (digit + 3).

Concept / Approach:

Check the defining properties. Gray code is not a numeric offset of binary; it is a different mapping designed for adjacency with Hamming distance 1. Excess-3, not Gray, uses the “+3” rule per decimal digit. Therefore the statement is false.

Step-by-Step Solution:

Verification / Alternative check:

Example for decimal 5: Excess-3 gives 1000 (since 5+3=8), while Gray(5) in 3-bit Gray is 111; clearly unrelated to a +3 offset model.

Why Other Options Are Wrong:

Choosing True would conflate two different coding schemes and ignore the adjacency design of Gray code.

Common Pitfalls:

Memorizing “+3” and misattributing it to the wrong code; forgetting that Gray code emphasizes transition reliability, not arithmetic offset.

Final Answer:

False