# Introduction

We are very comfortable with the decimal number system – in part due to the fact that we have ten fingers. Unfortunately, this is not a good system of numeration for digital computers and circuits, as our circuits are firmly based in binary – a system that works with two states – on and off.  This video chapter looks at how we can bridge the gap between our needs for decimal and the need for negative numbers and the fact that digital circuits are firmly based in binary.

## The 2’s Complement

The Two’s Complement is a method of representing negative/signed binary numbers that is commonplace in digital electronics and is the basis for how signed integers are represented in embedded systems. This tutorial explains the need for the Two’s Complement form and describes how you can perform operations such as additions/subtractions and multiplications using this form. It provides some numerical examples with solutions to allow you to test your understanding of the materials that are presented.

## Overflow and Underflow

In this video I will look at the problems that can arise in unsigned and signed systems with overflow and underflow, which is where our system goes beyond its physical limitations. I will look at how you can detect that overflow is occurring in a digital system and how you can design a logic circuit to detect its occurrence. The video then describes underflow and finally, presents a few interesting questions with solutions.