7.5 Dividing 2's complement integers
Just as multiplication can be turned into repeated additions, so division can be turned into repeated subtractions. And just as shifting a binary integer one place to the left equates to multiplying by two, so shifting a binary integer one place to the right equates to dividing by two.
Activity 27 (Exploratory)
How many places to the right do you think you would need to shift a binary integer to achieve division by eight?
You probably guessed that if shifting one place to the right is dividing by two then shifting two places to the right is dividing by four and shifting three places to the right is dividing by eight. And this is indeed the case.
Note that in integer arithmetic a fractional result is not possible. So if the divisor does not go exactly into the number to be divided then the result will have to be in the form of ‘it divides in such-and-such a number of times, with a remainder of such-and-such’.