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

# What is two's complement?

Two's complement is the most widely used representation of signed numbers. It provides ease of representation and computation. Unlike one's complement, **two's complement** has a unique representation for 0. Two's complement representation also has a sign bit on the extreme left.

Because there's a unique representation of $0$, the range of two's complement is larger than one's complement. The $0$ comes from the positive side representation, so the range of an $n$-bit two's complement number is:
-$2^{n-1}$ to $2^{n-1}-1$. Note that $n$ is usually a power of $2$.

Learn the representation of signed numbers in binary using two's complement.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Two's Complement

What is two’s complement?