Representing and manipulating data in computers
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

Representing and manipulating data in computers

7.6 Arithmetic with binary fractions

My final point in the preceding section brings home the fact that integer arithmetic is not really suitable when divisions are to be performed. It is also not suitable where some or all of the values involved in the arithmetic are not – or are not necessarily – integers, and this is often the case. In such cases, arithmetic has to be performed on non-integers.

The most common representation for non-integers is the floating-point representation that I mentioned briefly in Box 3. You may recall that numbers are represented in the form (mantissa × 2exponent), where the mantissa is a fixed-point fraction and the exponent a signed integer. Arithmetic with floating-point numbers may therefore involve calculations such as

(0.111 0001 × 210) + (0.000 1000 = 25)

(1.101 1000 × 2−5) − (1.000 1000 × 2−6)

(0.101 1100 × 215) / (0.111 0101 ×2−12)

Such arithmetic is by no means straightforward, and I have no intention of trying to show you how it is carried out. Most processors destined for PCs, workstations and other powerful computers include a ‘floating-point unit’ whose sole task is to carry out operations on floating-point numbers. If a processor without a floating-point unit is to be used to perform floating-point arithmetic then the software will have to take care of the complicated manipulations involved.


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus