Representing and manipulating data in computers

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

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?

Discussion

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’.

T224_2