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

# Multiplication technique

To multiply two's complement numbers we employ the same technique we used in the lesson [Multiplication in Binary](https://www.educative.io/courses/number-systems-for-computer-scientists/multiplication-in-binary), with some minor changes.

Before carrying out the multiplication, we *sign-extend* the number to twice as many bits. This simply means that we add $n$ copies of the sign bit to the left of the number, where $n$ is the number of bits in the original number. For example:

> $10001000$ would be sign-extended to $1111111110001000$.

After this, we carry out the multiplication as before. We take the $n$ **least-significant bits** of the product as our final answer.

Learn how to perform multiplication with two's complement numbers.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Multiplication With Signed Numbers

Multiplication technique