Imagine a clock face with numbers from 0 to y-1 then counting mod y is simply a process of advancing from number to number until you reach y-1 when you `roll over' to 0 and start the sequence again.

This definition is a bit more difficult to follow but it's still trivial as long as you studied `clock arithmetic' as part of modern maths at school. You can also think of it as doing the arithmetic modulo some number - so its the + or the * operators which are modified and the mod doesn't even appear. In this case the mod function is just a way of imitating what happens naturally when you do integer arithmetic using a fixed number of bits. Mod(x,y) or x % y implements finite arithmetic with This is much closer to the inner workings of the real machine: The active approach to mod considers what happens when you use it as part of basic arithmetic operations. it tells you the remainder after you have grouped x things into groups of size y. Whenever you have a problem that involves chopping something up into regular sized groups the mod function/operator comes in handy for working out how to deal with the leftovers. In this case you are thinking of working out what is left over if you do something in `chunks of y'.įor example, a text file is 20000 lines long and you can fit 66 lines to a page - how much text is left over? The answer is 2 because mod(20000,66)=20000 % 66 =2. Mod(x,y) or x % y gives the remainder when you The mod(x,y) function, or the mod operator x % y in Python, C# or JavaScript say, is very simple but you can think about it at least two different ways - corresponding, roughly speaking, to passive and active models of what is going on. As soon as you start implementing even the simplest of algorithms the need to understand mod will occur. You may not meet the mod function or operator in the course of learning to program, but once you start to write real code you will certainly meet it. Once you get away from the representation of numbers as bit strings and arithmetic via registers then many mod and remainder operations lose their immediate meaning so familiar to assembly language programmers. You find it in the way numbers are represented in binary and in machine code or assembly language instructions. Modular arithmetic used to be something that every programmer encountered because it is part of the hardware of every machine. Many programmers are puzzled by the mod, short for modulo, and integer division functions/operators found in nearly all languages. Not only is it the basis for many an algorithm, it is part of the hardware. The answer any experienced programmer should give you is 'a lot'. What has modular arithmetic got to do with the real world?

How to use mod