modular arithmetic

Discrete mathematics is the study of mathematics in systems that are countable, such as the set of integers.

Modular arithmetic is a topic of discrete mathematics that is defined as integer arithmetic. This means that there are no decimals. Most operations are very similar to "regular" arithmetic:

It actually gets tricky with division:

5 ÷ 3 actually equals 1.66666, but since there are no decimals, the result is truncated to the integer 1. The remaining .66666 is calculated using a new operator called modulo.

The result of the modulo operation is the remainder of the division. So, in our example:

   5    ÷    3    = 
(5 / 3) + (5 % 3) = 
   1    +  2 / 3  =
     1.66666

Note that the result of a modulo operation will always be an integer between 0 and the modulus minus 1. This special property is what makes modular arithmetic very useful in programming.

Math For Artists Who Now Need to Program

Elie Zananiri
ITP DriveBy
1 Oct 2008