Excess-3

Excess-3 (also known as Stibitz code) is a non-weighted binary code used to represent decimal numbers. It's a self-complementing BCD (Binary Coded Decimal) code, meaning that the 9's complement of a decimal digit can be obtained by inverting the bits of its Excess-3 representation.

The Excess-3 code for a decimal digit is derived by adding 3 to the digit and then converting the result to its binary equivalent. For example, the decimal digit 0 is represented as 0011 (binary for 3), the decimal digit 1 is represented as 0100 (binary for 4), and so on. The decimal digit 9 is represented as 1100 (binary for 12).

One of the main advantages of Excess-3 code is its ease of implementation in arithmetic operations, particularly subtraction, as it simplifies the handling of borrows. Because it is self-complementing, it simplifies subtraction by allowing the 9's complement to be easily determined. This was particularly important in early computing systems.

Excess-3 code is not widely used in modern computers, but it holds historical significance in the development of digital electronics and early computing. It serves as a good example of a BCD code with specific properties useful in specific applications.