Number System in Python

 

Python generally supports integers, fractional values and complex numbers and we have data types for them like int for integers, float for fractional values, and complex for complex numbers, we can understand that but if our computer wants to perform certain operations on bits or some other operations then we need to convert them into some number systems like binary, octal, hexadecimal. These are the three different number systems.

Number conversions are used in programming languages because we cannot directly use some operators like bit-wise operators, we need to convert decimals into binary and sometimes we need to convert binary format of a number to decimal, so we use number conversions there

Actually, number conversions are done on 4 types

1.      Decimal

2.      Binary

3.      Octal

4.      Hexadecimal

1. Decimal to binary:

                              Binary – which means 2, we can only use 2 digits 0 and 1 so we call them as binary digits nothing but bits.

So how to convert a number from decimal to binary

        Ex:  convert 25 to binary

                         0b011001

               Divide the given decimal by 2 and write down remainder aside and again do the division and again write down the remainder, keep on doing this until u get a number which is less than 2.

          So when we do the division 25 divided by 2 it gives us 12 as quotient and 1 as remainder , again when we divide 12 by 2 we get 6 as quotient  0 as remainder and again divide 6 by 2 we get 3 as quotient and 0 as remainder and again divide 3 by 2 we get 1 as remainder and 1 as quotient so quotient value became 1 which means it is less than 1 so we will stop the division , now from bottom  write remainders  one by one and till top number (bottom to top )

We will get like this 11001and add a zero before 1 then we will get output as 011001 this is the binary number of decimal numbers 25

     **** we also have an easy method to convert decimal into binary because we can’t do this all the time so computer will do this conversion for us, we just need to write a small syntax for decimal to binary conversion that is

               Syntax: bin(25)                                //bin() function gives us the binary format

                             0b011001

Where here we put ‘zero’,b, so that it represents that the given number is binary number.

2. Binary to decimal conversion:

                                                            If you want to convert a binary number to decimal number then you need to multiply every digit of the binary number with 2^x  where (x=0,1,2,3,4………)

And add all of them, I know u r a bit confused with this. let’s just see an example

 

                                0b011001

       0    1      1     0      0     1

                     2⁵ 24   2³   2²  2¹   2⁰

Now we need to multiply with each number and add all of them like this

                (0*32) + (1*16) + (1*8) + (0*4) + (0*2) + (1*1)                  where 2⁰ = 1

               = 0 + 16 + 8 + 0 + 0 + 1

               = 25

So, we got the output but this is also a long process so we will use the binary number in the IDE or IDLE

Then it will convert the given binary number and gives us the output in decimal number like this

 Example: 0b011001

                    25

Here we put ‘zero ‘b (0b), so that...Continuation