Class 7 - Number System

 Number System

1. Binary Number System

Only 0 and 1 are allowed in binary number system. So the base is 2(only two numbers)

e.g:

 (101)₂

2. Decimal Number System

0,1,2......9 are allowed in decimal number system. So the base is 10( 0 to 9,totally 10 numbers)
e.g:
(25)₁₀

The base is written along with the number to identify the number system.
Conversion from binary to decimal :
2⁰=1
2¹=2
2²=4 (2 x 2)
2³=8(2 x 2x 2)
2⁴=16(2 x 2x 2 x 2)
 and so on.......

2. (110)₂

1   1   0

 = 1 x 2 ² + 1 x 2 ¹+ 0 x 2 ⁰ 

 = 4 + 2 + 0
= 6

Answer = (6) ₁₀

3. (111)₂
 = 1 x 2 ² + 1 x   2 ¹   + 1 x   2 ⁰
= 4 + 2+ 1
= 7

4. (1011)₂
=1 x   2 ³  + 0 x 2 ² + 1 x   2 ¹   + 1 x   2 ⁰

= 8+0 + 2+ 1
= 11

5. (1101)₂
=1 x   2 ³  + 1 x 2 ² + 0 x   2 ¹   + 1 x   2 ⁰

= 8+4 + 0+ 1
= 13

Conversion from decimal to binary

This involves repeated division of the quotient by two, the remainder forms the part of the answer.
1. (4)₁₀

4 / 2 = 2  remainder = 0
2/2 = 1    remainder = 0

You cannot divide 1 by 2, so stop now. Therefore the answer is
=(100)₂

2. (7)₁₀

7 / 2 = 3 remainder = 1
3 / 2 = 1 remainder = 1

= (111)₂


3. (13)₁₀

13 / 2 = 6 remainder = 1
6 / 2 = 3   remainder = 0
3 / 2 = 1   remainder = 1
= (1101)₂