# Binary Number System

**The binary number system** is a number system that works with only 0 and 1. and only computers use this number system. because computers only know the ones and zeros. so it’s the base of number 2.

## What is a Binary number system?

The binary number system is a number system that represents the mathematical numbers in **zero (0)** and **one (1)**. it has only two symbols 1 for the maximum value and 0 for the minimum value of numbers.

for example, if I took the number 9 then the binary representation of number 9 is 1001.

**so, how do **we convert numbers into** the binary number?**

let’s take an example to understand the conversion. let’s say we have the number 9 which is a math number.

**so how can we represent 9 in a binary number?**

### Method to convert numbers into a binary number

To convert 9 into a binary number we divide the number 9 by 2. because a binary number is base of 2. as shown in the image given below.

So when we divide the 9 by 2. then the reminder we get is **1001**. and to convert the number 9 into a binary number. we need to arrange the remainder in the bottom to top or right-to-left manner.

so to arrange the remainder in the bottom to the top manner we get **1001**. so this is the binary representation of the number 9.

we can also convert a base 2 (binary number) to a decimal number. let’s take an example to understand it.

we have a binary number 1001. so to convert it into its equivalent decimal number we take a single digit of binary number from right to left and multiply with its equivalent base.

D(1001) = 1*2^{3} + 0*2^{2} + 0*2^{1} + 1*2^{0 }

D(1001) = 8 + 0 + 0 + 1

D(1001) = 9

### Working of Binary number system in Computer

to understand the working of the binary number system in the computer first we need to understand what is bits and bytes.

#### What are Bits and bytes?

We all work with base 10 numbers. and every mathematical condition is based on 10 numbers from 0 to 9. but the computer works with bits and bytes. so the bit is something called 0 or 1. and the 8 bit is equal to 1 byte.

[0][1]

we all have 10 numbers but the computer has only two numbers. a computer has only bits and bytes to work on it. it can be a **not(0)** or it can be **one(1)**. it cannot be the same at a time. it either be **one(1)** or either be **not(0)**.

**How do the Bits work in our hardware?**

Our computer is a very complex magnet. and bits are actually magnetic charges.** not(0)** is a negative charge and **one(1)** is the positive charge. by using the electronics computer we can work with base 2, **not(0)** and **one(1)**.

Our computer is a very delicate magnet. that’s why if we used a powerful magnet on our computer. we could potentially store wide data on a hard drive.

we can solve the data flows to our processor. so that’s why a bit has worked with two charges **negative(0)** and **positive(1)**.

**Note:** it’s only because the stick of a magnet on our computer is not a very good idea.

A bit is the smallest unit in a computer system. it is a basic unit of information in a computer system. using bit we manipulate and store the data in the computer system in memory. the bit is nothing but one or zero. If I say it in the simple form then

Bit = unit of information

#### Conversion of Bit into Byte

Let’s say I pick binary values which are 0 and 1. Then how we convert bit to byte is that

One Bit = 1

Two Bits = 01

Three Bits = 100

Eight Bits = 1001 1111 = 1 Byte

**Note:** here I pick the random values of bits. but why do we need to convert bits into bytes? if you don’t know then you must need to read the below lines.

Bits in a row have no real values. bits have only one(1) or not(0) and 1 value at a time. If a bit is 1 or only 0 it would be completely useless to us. the reason why we grouped the bits 0 and 1 is that when we grouped the bits 0 and 1. they represent the base 10 numbers.

On our calculator, we use only 10 base numbers. and how we add 999+888 and somehow the calculator works with base 2 numbers how to add these base 10 numbers together and print out the number on the screen add 999 and 888 we need to use a group of base two numbers. so that’s why we need to use a group of base two numbers. and the group of 8 bits is equal to one byte.

We know that there are some types of bits systems.

- 8-bit system.
- 16-bit system.
- 32-bit system.
- 64-bit system.

#### 8-bit system

In older times we used an 8-bit computer. it means that the computer is only able to process 8 bits at a time. it means we only used 8 once(1) and not(0) at a single time.

#### 16-bit computer

In 16-bit computers, we are only able to process 16-bit at a time. it means we used only 16 once(1) and not(0) at a single time.

#### 32-bit computer

In a 32-bit computer system, we are only able to process 32-bit at a time. it means we used only 32 once(1) and not(0) at a single time.

#### 64-bit system

Now we can work with the 64-bit system. it’s means now we can work with 64 bits or 64 once(1) or not(0) at a single time.

Also, Read