Excess-3 Code

Last Updated : 12 Aug, 2026

Excess-3 Code is an unweighted Binary Coded Decimal (BCD) code in which each decimal digit is represented by adding 3 to its BCD value.

  • It provides a unique 4-bit code for each decimal digit from 0 to 9.
  • Self-complementing property makes decimal complement operations simpler.

Representation of Excess-3 Code

The following table shows the BCD and corresponding Excess-3 (XS-3) code for each decimal digit. The Excess-3 code is obtained by adding 3 (0011) to the BCD representation of each digit.

Decimal Digit

BCD Code

Excess-3 Code

0

0000

0011

1

00010100

2

00100101

3

00110110

4

01000111

5

01011000

6

01101001

7

01111010

8

10001011

9

10011100

Note: The binary values 0000 and 1111 are not assigned to any decimal digit in Excess-3 code.

Solved Examples

Example 1: Decimal Number 9

BCD of 9 = 1001

Add 0011 (3):
1001 + 0011 = 1100

Excess-3 code of 9 = 1100

Example 2: Decimal Number 15

Convert each digit separately:

  • 1 → 0001 + 0011 = 0100
  • 5 → 0101 + 0011 = 1000

Excess-3 code of 15 = 0100 1000

Example 3: Decimal Number 6

BCD of 6 = 0110

Add 0011 (3):

0110 + 0011 = 1001

Excess-3 code of 6 = 1001

Advantages

  • Simplifies Decimal Arithmetic: The self-complementing property makes decimal subtraction and complement operations easier to implement.
  • Unique Representation: Every decimal digit has a unique 4-bit code, reducing ambiguity during encoding.
  • Easy Error Detection: Invalid code combinations can help identify errors during data processing.
  • Compatible with Digital Systems: Excess-3 works well with BCD-based digital circuits that process decimal numbers.

Disadvantages

  • Requires Extra Conversion: Decimal digits must first be converted to BCD and then adjusted by adding 3.
  • Uses More Processing Steps: Additional conversion increases the complexity compared to standard binary representation.
  • Limited Use in Modern Systems: Most modern computers prefer pure binary or standard BCD over Excess-3.
  • Designed Only for Decimal Numbers: It is not suitable for representing non-decimal number systems.

Applications

  • Electronic Calculators: Excess-3 was widely adopted in early calculators to simplify decimal calculations.
  • Decimal Arithmetic Circuits: It makes operations such as decimal addition and subtraction easier to implement.
  • Digital Communication: The unique code combinations help reduce the chances of incorrect decimal representation during data transfer.
  • Learning Digital Electronics: Excess-3 is commonly taught to explain BCD coding and different decimal coding techniques.
  • Decimal-Based Systems: It is suitable for applications where decimal values need to be represented accurately.
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