Excess-3 (XS-3) coding — determine the correctness of the statement: “When using the excess-3 code, a value of 3 is added to each decimal digit before converting that digit to a 4-bit binary code.”

Introduction / Context:Excess-3 (XS-3) is a self-complementing binary-coded decimal (BCD) scheme commonly introduced in number systems and digital logic. Understanding its construction helps with error detection properties and complements in arithmetic operations. This question asks whether the coding rule indeed adds 3 to each decimal digit before encoding in binary.

Given Data / Assumptions:

• Each decimal digit (0–9) is encoded independently.
• Excess-3 is a 4-bit code for each decimal digit.
• “Add 3 then convert to 4-bit binary” is the proposed rule.

Concept / Approach:In XS-3, every decimal digit D is mapped to D + 3, and this sum is then encoded as a 4-bit binary number. For example, 0 → 3 (0011), 5 → 8 (1000), 9 → 12 (1100). The “excess” of 3 yields a self-complementing property: the 9’s complement of a decimal digit corresponds to the bitwise complement of its XS-3 code, simplifying certain arithmetic and error checks.

Step-by-Step Solution:

Verification / Alternative check:Look-up tables in textbooks match these results; decoding reverses the process by subtracting 3 from the 4-bit value to recover the decimal digit.

Why Other Options Are Wrong:

• Incorrect / Only true for odd digits / Only true for digit 9: The rule applies uniformly to all digits 0–9.

Common Pitfalls:Confusing XS-3 with straight BCD (8421) where no “+3” offset exists; forgetting that each digit is encoded independently and must remain in 4 bits.

Final Answer:Correct — Excess-3 encodes each decimal digit as (digit + 3) in 4-bit binary.