Number System and Conversions

Number System and Conversions:

Number Systems:

• Binary Number System ( 0-1 )

• Octal Number System ( 0-7 )

• Decimal Number System ( 0-9 )

• Hexa-Decimal Number System ( 0-9,A-F )

Interpreter Takes input as any Number system  and produce the output as only Decimal Number System.

We can give the any number system number as a input to the variables in python, By giving the special characters at the beginning of the number.

Special Characters are:

• 0b  for Binary Number System. example: x= 0b1010

• 0o    for Octal Number System. example: y=0o257

• no-specify  for Decimal Number System. example : z= 1569

• 0x  for Hexa-Decimal Number System. example : a= 0x28CE

NOTE:

• Here 0 means zero, not a character

Binary Number System:

• The base or radix of binary number system is 2.

• The possible digits that are used in binary number system are 0 and 1

• We can give the input values in the form of binary numbers format by giving ob as prefix.

Example 1:

      >>> x=0b1010    -----> Binary value

      >>> print(x)

      10   -----> Decimal value

Explanation:

Converting binary number to Decimal number

                1010 =1*2*2*2  +  0*2*2  +  1*2  +  0*1

                         =8+0+2+0

                         =10

Example 2:

        >>> x= 0b1020

       SyntaxError: invalid syntax

Octal Number System:

• The base or radix of octal number system is 8.

• The possible digits that are used in octal number system are 0 to 7.

• We can give the octal number system number as input by giving 0o beginning of the number.

Example 1:

             >>> y= 0o123           -----> Octal number

             >>> print(y)

             83       ------> Decimal number

Explanation:

                    123     = 1*8*8  +  2*8  +  3*1

                               = 64+16+3

                               = 83

Decimal Number System:

• The base or radix of decimal number system is 10.

• The possible digits that are used in decimal number system are 0 to 9.

• The default number system followed by the python is decimal number system.

Example 1:

                  >>> z=1234     ----> Decimal number

            >>> print(z)

              1234               -----> Decimal number

Explanation:

                 1234 = 1*10*10*10  +  2*10*10  +  3*10  +  4*1

                          = 1000+  200 +  30  +  4

                          = 1234

Hexa-Decimal Number System:

• The base or radix of  hexa-decimal number system is 16.

• The possible digits that are used in hexa-decimal number system are 0 to 9 and A to F.

• We can give the hexa-decimal number system number as input by giving 0X as prefix.

Example 1:

                >>>  a= 0x25      ------> Hexa-Decimal number

             >>> print(a)

                37                   ------> Decimal number

Explanation:

                   25 = 2*16  +  5*1

                        = 32+5

                        = 37

Note:

• We can give any number system number as input but we will get the output in the form of decimal number system format by default.

Number System Conversions:

By using pre-defined functions we can display the any number in the form of any number system format.

Pre-defined functions are:

• bin( ) -----> for binary Number system.

• oct( ) ------> for Octal Number System.

• hex( ) -----> for Hexa-Decimal Number System.

Example 1:

Binary number to octal, decimal and hexa-decimal number.

          x=0b1010                # input is binary number        

        print(oct(x))            #octal number

        print(x)                   # decimal number

        print(hex(x))          # hexa decimal number

Output:

                     0o12

                10

                0xa

Example 2:

Octal nuber to Binary,decimal and hexa-decimal number.

                x=0o123           # input is octal number

                print(bin(x))     # binary number

                print(x)            #  decimal number

                print(hex(x))   #  hexa decimal number

Output:

               0b1010011

               83

               0x53

Example 3:

Decimal number to Binary, Octal and Hexa-decimal number.

          x=157                      # input is decimal number.

         print(bin(x))            #binary number.

         print(oct(x))            # octal number.

         print(hex(x))           # hexa decimal number.

Output:

        0b10011101

        0o235

        0x9d

Example 4:

Hexa-Decimal number to Binary,Octal and Decimal number.

         x=0x2b5c         # input is hexa-decimal number.

         print(bin(x))    #binary number.

         print(oct(x))    # octal number.

         print(x)           #  decimal number.

Output:

          0b10101101011100

          0o25534

          11100

Note:

•  in python  #  represent Comment.

Note:

•  Decimal point numerical values (Float Values) can be represented in the form of decimal  number system only.