Excess-3, ASCII, and Other Digital Codes

Excess-3 Code (XS-3)

Excess-3 is obtained by adding 3 (0011) to each BCD digit. It is a non-weighted, self-complementing code.

Self-complementing property: 9's complement of a digit = 1's complement of its XS-3 code.

• Digit 3 = 0110 in XS-3; 1's complement = 1001 = XS-3 of 6 (which is 9-3=6 ✓)
• This makes subtraction easier in BCD arithmetic.

Conversion Example: Convert 47 to XS-3:

Parity Code

A parity bit is appended to make the total number of 1s either even (even parity) or odd (odd parity).

Even parity example: Data = 1011010 Count of 1s = 4 (already even) → parity bit = 0 Transmitted: 10110100

Odd parity example: Data = 1011010 Count of 1s = 4 (even, need odd) → parity bit = 1 Transmitted: 10110101

Limitation: Parity detects single-bit errors only. Double-bit errors go undetected.

Comparison of Common Codes

Interview Questions

Q1: Why is Excess-3 called self-complementing? The 9's complement of any digit d is (9-d). In XS-3, the 1's complement of the XS-3 code of d gives the XS-3 code of (9-d). This allows 9's complement subtraction using simple bit inversion, useful in BCD arithmetic without a separate complementing circuit.

Q2: What is the difference between ASCII and Unicode? ASCII uses 7 bits (128 characters) for English. Extended ASCII uses 8 bits (256 characters). Unicode uses 8–32 bits (UTF-8, UTF-16, UTF-32) to represent all languages — over 1 million code points. Modern systems use UTF-8 which is backward compatible with ASCII.

Q3: Convert ASCII code 0x41 to character. 0x41 = 65 decimal = 'A'.

Q4: What is an alphanumeric code? A code that represents both letters (alpha) and numbers (numeric), plus special characters. ASCII is the most common alphanumeric code. It's used in keyboards, file systems, and communication protocols.