EXCESS -3 Code

Описание: Excess-3 code is a non-weighted binary code used to represent decimal numbers. It is derived by adding 3 to each digit of the decimal number before converting it to its 4-bit binary equivalent. This code is considered self-complementing, meaning the 1's complement of an Excess-3 number represents the 9's complement of the original decimal number.
Here's how Excess-3 code works:

Add 3: For each decimal digit you want to encode, first add 3 to it.

Convert to Binary: Then, convert the resulting decimal number to its 4-bit binary representation.
Example:

To represent the decimal digit 5 in Excess-3, add 3: 5 + 3 = 8.

Convert 8 to binary: 1000.
Therefore, the Excess-3 code for 5 is 1000.

Key characteristics of Excess-3 code:

Non-weighted:
Unlike BCD (8421) code, Excess-3 doesn't have fixed positional weights.

Self-complementing:
The 1's complement of an Excess-3 number results in the Excess-3 representation of the 9's complement of the original decimal number, according to eeeguide.com.
Used in Arithmetic:
Excess-3 code simplifies certain arithmetic operations, particularly subtraction, in digital systems.
Invalid Code Groups:
Excess-3 code does not utilize all 16 possible 4-bit combinations. Code groups like 0000, 0001, 0010, 1101, 1110, and 1111 are considered invalid

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