Number System: Binary, Octal, Decimal, Hexadecimal, and conversion between different number systems

 Number System

Each number system has a base also called a Radix. A decimal number system is a system of base 10, binary is a system of base 2, octal is a system of base 8, and hexadecimal is a system of base 16. 

These bases are the maximum number that the numbering system allows. For Example in base 10, we can count from 0 to 9, that is,10 digits. 

Conversion between different Number Systems

Decimal To Binary

Method to convert a Decimal number into its Binary equivalent:
1. Divide the decimal number by 2.
2. Take the remainder and write it on the other side.
3. Again divide the quotient by 2.
4. Repeat the same process until the decimal number cannot be divided further.
5. Write the remainders in reverse order and you get the resultant binary number. 

Example : 

Q1: Convert the Decimal number 201 into its Binary equivalent.

201 / 2 = 100          1

100 / 2 = 50            0

50 / 2 = 25              0

25 / 2 = 12              1

12/ 2 = 6                 0

6 / 2 = 3                  0

3 / 2 = 1                  1

1 / 2 = 0                  1

Answer: (11001001)2

Fractional Decimal to Binary

The conversion of the number before the point is similar to the above method but the conversion of the number after the point is done differently. 

Example

Q. Convert Decimal number 201.47 into its binary equivalent.

The binary for 201 is simply done in the above example. So, (201)10  = (11001001)2

Let us convert (0.47)10 

 

Multiply 0.47 By 2                                                         0.94

Again multiply fraction part 0.94 by 2                             1.88

Again multiply fraction part 0.88 by 2                             1.76

Same as above 0.76 X 2                                                1.52

Same, 0.52 X 2                                                             1.04

Repeat this process until the fraction part become 0. But like above in some cases, it can be a long process so we will calculate only 5-6 digits. And write all integer values from top to bottom.

So, the Final Result is (201.47)10 = (11001001.01111)2