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

# How does it work?

Just like scientific notation is an extension of the decimal point notation, floating points can be said to extend fixed point notation.

Let's look at a number in scientific notation:
> $s$ $m \times 10^{n}$

We can divide this number into three distinct parts:
- The coefficient $m$, known as the *significand* or the *mantissa*, which can be any *real number*
- The power of $10$, $n$, which is called the *exponent*, and can be any $integer$ (positive or negative)
- $s$, which is the *sign*, and can be $-$ or $+$.

In the decimal representation, we leveraged extra symbols like $\times$, the sign, and exponent. In binary, we need to encode all of this in a string of ones and zeroes. For this we develop some conventions of how a floating point number will be represented.

Learn about the conventions behind floating point representation.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Floating Point Representation

How does it work?