Modular arithmetic is all about finding the remainder from long division (MOD), and the total number of times that a number goes into a division (DIV). Let's take a look at a quick example of 10 divided by 7 (you might want to remind yourself about long division):

    1 r 3
 7)10
    7
    3

Hopefully that wasn't too hard. We now need to introduce some terminology, MOD and DIV:

• MOD = finds the remainder from long division i.e. 10 MOD 7 = 3
• DIV = finds the number of divides in long division i.e. 10 DIV 7 = 1

Hopefully you are now pretty good with MOD and DIV, but what exactly is the point of all this? A very common example in past exam paper has been using the MOD and DIV to work out a binary equivalent of a denary number.

Note that Visual Basic does not have a DIV function and uses A\B instead

sub convertDtoB(byVal base10 as integer)
  dim base2(7) as integer 'create an array to store the binary
  dim temp as integer = base10
  for i = 7 to 0 step -1 'loop through each binary bit starting from the biggest value
    base2(i) =  temp \ (2^i)  'temp DIV 2^i
    temp = temp MOD 2^i
  next
  console.write(base10 & " in binary = ")
  for i = 7 to 0 step -1 'loop through each binary bit starting from the biggest value
    console.write(base2(i))
  next
end sub

67 in binary = 01000011

Another common use is in finding out whether a number is odd or even using the MOD function. We know that MOD returns the remainder from a division sum. So for example 4 MOD 2 = 0, 5 MOD 2 = 1, 6 MOD 2 = 0 and so on. By modding something with 2 we can work out whether it is odd or not due to the return value.

Dim testNum as Integer
Dim temp as Integer
console.writeline("please insert a number to test:")
testNum = console.readline()
If testNum MOD 2 = 0 Then
  Console.Writeline("The number is even")
Else
  Console.Writeline("The number is odd")
End If