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Formation of Binary numbers

                 As you know the binary number system consists of two digits: 0 and 1 and its base is 2. Each digit
                 or bit in a binary number system can 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
                         4
                                               2
                                                          1
                                    3
                                                                     0
                 = (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 formed using 0, 1, 2, 3, 4, 5, 6 and 7.
                 The base of the octal number system is 8. It is also known as the base-8 system. Each positioning
                 number represents the power of base 8.
                 For example: (1763)
                                     8
                                                          0
                         3
                                    2
                                               1
                 = (1 × 8 ) + (7 × 8 ) + (6 × 8 ) + (3 × 8 )
                 = (1 × 512) + (7 × 64) + (6 × 8) + (3 × 1)
                 = 512 + 448 + 48 + 3
                 = 1011 or (1011)
                                  10
                 Hexadecimal Number System

                 A number system made up of sixteen symbols, 0 to 9, and A to F is known as the hexadecimal
                 number system. When the hexadecimal number system is used, every number is formed using 0,
                 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where A = 10, B = 11, C = 12, D = 13, E = 14, and F =
                 15. The base of the hexadecimal number system is 16. It is also known as the base-16 system. Each
                 position represents a power of base 16.

                 For Example: (2AF)                       Info Byte
                                    16
                                                 0
                          2
                                      1
                 = (2 × 16 ) + (A × 16 ) + (F × 16 )        Name Size (bits)                 Examples
                 = (2 × 256) + (10 × 16) + (15 × 1)        Bit           1       Single digit either 0 or 1
                                                           Nibble        4       Group of 4 digits either 0 or 1
                 = 512 + 160 + 15                          Byte          8       Group of 8 digits either 0 or 1
                                                           Word          16      Group of 16 digits either 0 or 1
                 = (687)
                        10


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                                                                                               Number System
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