Terminology » BCD Code vs. Excess-3 Code: Key Differences Explained

BCD Code vs. Excess-3 Code: Key Differences Explained

binary code bcd excess-3 data representation digital logic

This article clarifies the core differences between BCD (Binary Coded Decimal) code and Excess-3 code. Let’s dive in!

BCD stands for Binary Coded Decimal. It’s a way to represent decimal numbers (0-9) using binary code.

Table 1 illustrates the conversion between BCD inputs and their corresponding Excess-3 code outputs.

BCD vs. Excess-3 Code Conversion Table

DecimalBCD (A, B, C, D)Excess-3 (W, X, Y, Z)
000000011
100010100
200100101
300110110
401000111
501011000
601101001
701111010
810001011
910011100

BCD vs Excess-3 code

As you can see, Excess-3 code output is obtained by simply adding 0011 (decimal 3) to the BCD data input.

Example:

  • BCD Input: 0000
  • Excess-3 code Output: 0011

Boolean Functions for Excess-3 Code Outputs

The minimized boolean functions for each bit of the Excess-3 code output (W, X, Y, Z) are as follows:

  • Z = D’ (D complemented)
  • Y = C*D + C’*D’
  • X = B’*C + B’*D + B*C’*D’
  • W = A + B*C + B*D