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

# Shift operations

Shift operations involve *shifting* the bits in a binary number to the left or right. Thus they are appropriately named **right shift** and **left shift**.



# Left shift

Left shifting a binary number is equivalent to multiplying it with $2$. A left shift is represented with **<<**.

To perform a left shift by $1$ we:
- Remove the most significant bit
- Append a $0$ as the least significant bit

For example:
> $0010$ << $1$ = $0100$

We can see that $2$ left shifted by $1$ is $4$. We can also perform multiple left shifts:

> $0010$ << $2$ = $1000$

This is just like performing another left shift on the answer of the previous example.

Let's look at another example:

Learn what shift operations are, and what they're used for.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Shift Operations

Shift operations

Left shift