**The binary number system** is a numbering system that works with only two unique digits 0 and 1. The binary number system is used by only computers. To represent electronic circuit voltage states, (i.e., on/off switch), which considers 0 voltage input as off and 1 input as on. It is also known as the base-2 number system.

## 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 0 and1. we use 1 for maximum value and 0 for a minimum value of numbers.

For example, we have a number 9, then the binary representation of number 9 is 1001.

**So how we convert numbers to binary numbers.**

Let’s take an example to understand **how we convert numbers to binary numbers.** let’s say we have the number 9, which is a math number. Now the question is, How we can represent 9 in a binary number.

### Method to convert numbers into a binary number.

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

So when we divide the number 9 by 2. Then the reminder we get is **1001**. To convert number 9 into a binary number. We arrange the remainder in the **bottom to top** or **right to left** approach.

So to arrange the remainder in the bottom to the top approach. We get the binary number **1001**.By this is the binary representation of number 9.

We can also convert a base 2 (binary number) to a decimal number.

For example.

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 it 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

Before, to understand the working of the binary number system. First, we need to understand about the bits and bytes.

#### What are Bits and bytes

We all are work with base-10 numbers. The every mathematical condition based on 10 numbers from 0 to 9. The computer works with bits and bytes.

So the bit is also 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 work with only bits and bytes. It can be a **not(0)** or it can be **one(1)**. It cannot be the same at a time, either be **one(1)** or either be **not(0)**.

__How do the Bits work in our hardware?__

__How do the Bits work in our hardware?__

Our computer is a very complex magnet, and bits are magnetic charges.** **A** Not(0)** is a negative charge, and **one(1)** is the positive charge.

As we use, electronics computer, we can work with base 2, **not(0)** and **one(1)**.

Our computer is a very delicate magnet. This is a reason if we used a powerful magnet on our computer. We could potentially store-wide data of hard drives.

We can solve the flow of the data to our processor. So the bit has worked with two charges, **negative(0)** and **positive(1)**.

** Note:** it’s only because of 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. We use bits to manipulate and store the data in the computer system in memory. The bit contains two values one(1) or zero(0). If I say in the simple form is.

Bit = unit of information.

#### Conversion of Bit into Byte

For example,

I pick binary values, which are 0 and 1. let’s see, how we convert bit to byte is that.

One Bit = 1

Two Bits = 01

Three Bits = 100

Eight Bits = 1001 1111 = 1 Byte

Note:

Now, I pick the random values of bits.

Note:

Bits in a row has not 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 work with base 2 number. How to add these base 10 numbers together and print out the number on the screen. Add these 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-bit 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 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 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.

Thank you,

I hope you found this article helpful.

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