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Binary Number System

                 A number system made up of only two digits: 0 and 1, is known as the binary number system.
                 In the binary number system, every number is represented using the digits 0 and 1. The word
                 binary comes from ‘Bi’ meaning two that’s why the base of the binary number is 2. It is also
                 known as the base-2 system.

                                 Name      Size (bits)                    Examples

                                Bit             1        0 or 1

                                Nibble          4        1010, 1001
                                Byte            8        10101010, 11110011

                                Word            16       1010101010101010, 1111000011110011

                 Formation of Binary numbers

                 Each digit or bit in a binary number system can either be 0 or 1. A combination of binary digits
                 may be used to represent different quantities like 1001. The positional value of each digit in a
                 binary number is twice the place value or face value of the digit on its right side. The weight of
                 each position is a power of 2. The place value of the digits according to position and weight is
                 as follows:


                           Position       3         2         1          0                  –1         –2
                                                                                   .
                           Weight         2 3       2 2       2 1       2 0                 2 –1      2 –2

                 For example: 10101 or (10101)  is
                                                 2
                                                          1
                         4
                                    3
                                                                     0
                                               2
                 = (1 × 2 ) + (0 × 2 ) + (1 × 2 ) + (0 × 2 ) + (1 × 2 )
                 = (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1)
                 = (21)
                       10
                    Info Byte
                     If the last digit of a binary number is 1, the number is odd; if it is 0, the number is even.


                 Octal Number System

                 A number system made up of eight digits from 0 to 7, is known as the octal number system.
                 When the octal number system is used, every number is represented using the digits 0 to 7. The
                 base of the octal number system is 8. It is also known as the base-8 system. In the octal number
                 system, each digit’s position represents a power of 8.

                 The place value of the digits according to position and weight is as follows:

                                Position       3         2         1                   –1        –2
                                                                              .
                                Weight         8 2       8 1       8 0                 8 –1      8 –2

                 For example: (1763)
                                     8
                         3
                                                          0
                                               1
                                    2
                 = (1 × 8 ) + (7 × 8 ) + (6 × 8 ) + (3 × 8 )
                                                                                                                  23
                                                                                               Number System
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