binary number system

What is Binary Number System and How Its work?

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.

Binary number system and it's working in computer

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.

Binary number system

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*23 + 0*22 + 0*21 + 1*2
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?

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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Reference:

medium.com

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