Gain insights into essential number systems for computer scientists. Explore binary representation, and learn to represent and manipulate positive, negative, and fractional numbers stored in computers.

Get introduced to the number systems that are essential for computer scientists, and take a deep dive into binary representation. Learn how to represent and manipulate, positive, negative, and fractional numbers in binary, and learn how numbers are stored and represented in computers.

The only background this course requires is grade-school arithmetic. No programming knowledge is needed.

Number Systems For Computer Scientists

# Arithmetic with two's complement

A powerful aspect of two's complement representation is the ease with which we can carry out addition and subtraction.
> The decimal property $a - b = a + (-b)$ can essentially be extended to two's complement as well.

This means that the computer can use the same tools for two's complement subtraction as it does for addition. One's complement subtraction on the other hand requires complex circuitry.

Let's go through an example of addition and an example of subtraction.

Learn how to do addition and subtraction in binary using two's complement numbers.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Arithmetic with Signed Numbers

Arithmetic with two’s complement