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

We have seen how we can represent a range of numbers in the language of computers, $1$'s and $0$'s. But we know that numbers aren’t the only thing that we can represent in a computer. So, there is still something missing when we think about how a computer understands what to display on the screen when we type a letter like "*a*", or a symbol like "&" using the keyboard. 

The answer is **ASCII**.

ASCII is simply a system that encodes letters and common symbols as decimal numbers. These numbers can then easily be represented and stored by a computer.  

# How does it work?

ASCII uses **$7$ bits** to represent one displayed character. The idea is to create a convention for encoding each character with one $7$-bit number.

Because one byte has $8$ bits, we have $2^7 = 128$ different options to encode. We use them to encode uppercase and lowercase letters of the English alphabet, along with some common symbols. The encodings are divided into two parts; the printable characters and the control characters.

## Control characters

The first $32$ ASCII numbers ($0000000-0011111$) are called control characters. These cannot be displayed on the screen and they are used for different computer commands.

Learn about ASCII, which makes representing letters with a computer possible.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

ASCII

What is ASCII?

How does it work?