Binary Number System Explained

Binary ? It's a number system that represents data. As u know Computer system only understand the language of 0 & 1 which we say binary.

Why computer understand only 0 & 1 (binary)?

Because it's works with electrical signals which can only be two ON or OFF, 1 or 0 respectively.

Binary digits represent data( image, text, audio, video etc..) in bits,

1 bit can store either 1 or 0.

1 byte = 8 bits

1 kilobytes (KB) = 1024 bytes

1 megabytes (MB) = 1024 KB & so on .....

Binary number are based on powers of 2, also we can say that binary notation is base 2 notational system.

What is meant by power of 2 ?

Simply it means multiples of 2,

Example-(21= 2×1=2 , 22=2×2=4, 23=2×2×2=8 & so on)        

Relation between decimal & binary-

Decimal system use base 10, or power of 10.

Example: 123 = 1×102=100 + 2×101=10 + 3×10?=3         

Binary system use base 2, or power of 2.

Example: 101 = 1×22=4 + 0×21=2 + 1×2?=1         

Applying power of 2 from left to right.(Rule)

Conversion of decimal to binary -

1. Divide decimal number by 2.

2. Note reminder either 0 or 1

3. Divide until the quotient is 0.

4. Write remainders in reverse order.

Example : decimal 13 to binary

13÷2 = 6 reminder 1

6÷2 = 3 reminder 0

3÷2 = 1 reminder 1

1÷2 = 0 reminder 1

Note reminder in Reverse oder 1101 which is a binary number of decimal 13.

Conversion of binary to decimal

1. Write down the binary number.

2. Multiply each bit by Power of 2

Power from the right to left (starting from 0).

3. Add all

Example : convert 1101 binary to decimal

1101 = 1×23=8 + 1×22=4 + 0×21=0 + 1×2?=1 (8+4+1=13)         

I hope everything is cleared now.

Let us understand practical uses which is much more important than all.

1. Data representation like text image video audio etc ...

In text binary uses ASCII code which is defined for every char no. Etc .

Like if u press "A" binary uses ASCII code 'A' = 01000001 (in binary) to understand this.

In images pixels (RGB values) values are stored in form of binary.

In video audio etc.. signals Amplitude is stored in the form of binary.

2. Data transfer, transmission of voice calls, biometric scanners, QR codes, electrical appliances digital appliances etc.

Note: we are not going much deeper in it because it's not that much required, A basic overview is enough.

ASCII BINARY & DECIMAL RELATION.

Feel free to ask, if have any doubts related with this.