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

                                 Position       3         2         1         0                   –1        –2
                                                                                         •
                                 Weights       2 3        2 2       2 1       2 0                 2 –1      2 –2

                              Factbot

                       A single binary digit (like '0' or ‘1’) is called a ‘bit’. For example, 11010 is five bits long. The word bit is made
                       up of the words 'binary digit’.

                     Octal Number System

                     The octal number system consists of eight digits from 0 to 7. Hence, the octal number system's base
                     is 8. In this system, each digit's position represents a power of 8. In this system, any digit is always less
                     than 8. The octal number system serves as a concise representation of lengthy binary numbers. The
                     number (841)  is not valid in this number system as 8 is not a valid digit.
                                  8
                     Hexadecimal Number System

                     The hexadecimal number system consists of 16 digits from
                                                                                       The decimal number system is based
                     0 to 9 and letters from A to F. The letters A to F represent     on ten digits, which is likely influenced
                     decimal numbers from 10 to 15. This number system has a             by the number of human fingers.

                     base of 16. Each digit position in the hexadecimal number
                     system represents a power of 16.

                     For example, the number  (764)  is a valid  hexadecimal
                                                      16
                     number. It is different from (764)  which is seven hundred and sixty four.
                                                      10
                     This number system provides shortcut methods to represent long binary numbers.

                     DECIMAL TO BINARY CONVERSION

                     To convert a decimal number into a binary number, follow these steps:

                        Divide the decimal number by 2 (the base of the binary number system).

                        Note down the quotient and remainder.
                         Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.

                         Repeat the procedure until the quotient is less than 2.

                         List the last quotient and all the remainders (moving from bottom to top). You will get your binary
                       number.

                     Look at the given examples to understand the conversion better.

                                                                        Number Systems & Binary in Computing and AI     71

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