Binary Number System

       
           

Numbers with base value 2 are known as binary numbers. They are represented using two digits i.e. 0 and 1. For example: 01011 represents (0 × 24) + (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20), they represent 0 + 8 + 0 + 2 + 1, and equals to 11. Now we will see how we will represent the digits in binary notation.
 

Decimal Number

Binary Number

0

0000

1

0001

2

0010

3

0011

4

0100

5

0101

6

0110

7

0111

8

1000

9

1001

10 (A)

1010

11 (B)

1011

12 (C)

1100

13 (D)

1101

14 (E)

1110

15 (F)

1111

16 (10)

10000

 

Now we will see how to convert a number represented using Binary Number System to decimal number. Suppose we have 100101 which is in binary form. As we discussed above binary number is always written in 0 and 1 form. So we can convert it into decimal form as:

Given number is 100101, we can write given number as:

[(1) x 25] + [(0) + 24] + [(0) x 23] + [(1) x 22] + [(0) x 21] + [(1) x 20] on further solving we get:

= [1 x 32] + [0 x 16] + [0 x 8] + [1 x 4] + [0 x 2] + [1 x 1],

= 32 + 0 + 0 + 4 + 0 + 1 = 37.

This is how we convert binary numbering system to decimal number.
Now we will see the addition procedure of binary number.
  

0 + 0

0

0 + 1

1

1 + 0

1

1 + 1

0

Using these conditions we can add binary numbers. 

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