Odometer Simulation - Encoding Negative Numbers

This is a simulation intended to demonstrate the problem with encoding negative numbers in a computer system. It was created to use a starter activity with a sixth form class prior to teaching sign & magnitude, ones complement and twos complement encoding.

The PowerPoint file includes instruction on slide 1. The rest of the ppt shows a dial such as you might find in a car odometer (or a combination lock, date stamp, etc) with numbers. The slides show they can be ‘dialed’ forwards or backwards. When dialled backwards past zero we get 9, not -1 because there is no negative symbol available. This is the same problem in a computer system. We have only 0 and 1, we don’t have a negative symbol available. So how do we ‘encode’ a negative number?

It is also effective to have some code locks or date stamps available to give students to demonstrate the principle for themselves.

This then leads into a problem solving discussion where the teacher can then introduce the idea of sign & magnitude one ones/twos complement.