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

## Fractions in binary

We have learned how to represent whole numbers – positive and negative – in binary, and how to divide with binary numbers, but you might be wondering how we would represent fractions.

Representing fractions in binary is essential because we need fractions when simulating many real-world scenarios using computers.

Let's have a look at the decimal technique of representing non-integer numbers:
> For every place beyond the decimal point, i.e., on the right of the units ($10^0$) place, the value is equivalent to $\frac{1}{10^n}$. The first place after the decimal has a place value of $10^{-1}$ or $0.1$, the second place has $10^{-2}$ or $0.01$, and so on.

So place values on the left of the decimal point increase in powers of $10$, and decrease in powers of $10$ to the right. Can we propose something similar for the binary system? There are two methods for representing fractional numbers in binary. One is **fixed point notation**, which we will look at in this lesson, and the other is **floating point notation**, which we will look at in the rest of this chapter.


# Fractions in binary

We have learned how to represent whole numbers – positive and negative – in binary, and how to divide with binary numbers, but you might be wondering how we would represent fractions.

Representing fractions in binary is essential because we need fractions when simulating many real-world scenarios using computers.

Let's have a look at the decimal technique of representing non-integer numbers:
> For every place beyond the decimal point, i.e., on the right of the units ($10^0$) place, the value is equivalent to $\frac{1}{10^n}$. The first place after the decimal has a place value of $10^{-1}$ or $0.1$, the second place has $10^{-2}$ or $0.01$, and so on.

So place values on the left of the decimal point increase in powers of $10$, and decrease in powers of $10$ to the right. Can we propose something similar for the binary system? There are two methods for representing fractional numbers in binary. One is **fixed point notation**, which we will look at in this lesson, and the other is **floating point notation**, which we will look at in the rest of this chapter.


Learn how to represent numbers with fractional parts using fixed point notation.

Introduction

Essential Number Systems

Some Binary Operations

Signed Binary Numbers

Representing Numbers With Fractional Parts

Representation in a Computer

Conclusion

Fixed Point Notation