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01


                                                                                   NUMBERS

















                        Learning Objectives


                    1.1  Number System                                1.2  Number System Conversion
                    1.3  Binary Arithmetic                            1.4  Octal Arithmetic
                    1.5  Hexadecimal Arithmetic



                 In order to quantify any set of objects or keep account of lunar cycles, the concept of counting started in prehistoric age.
                 Initially counting was done using pebbles, sticks, bones, etc. where each stick, pebble or bone represented one object.
                 Tally stick counting method was also practised by making marks or cutting notches into pieces of wood, or even tying
                 knots in string. With advancement of human civilisation, the requirement to represent larger numbers increased. The
                 need for better representations, lead to development of different number systems. The most scientific one being the
                 positional number system.

                     1.1 NUMBER SYSTEM
                 According to early sources, the Babylonians introduced the positional system, in which the place value of the numerical
                 systems was established. The positional system was further modified in Hindu Arabic number system which was
                 developed during Gupta period. It also introduced the concept of decimal point. This number system is still used for
                 the symbolic representation of numbers and is known as Decimal number system.

                                                               Definition


                       A number system is defined as the representation of numbers by arranging digits or symbols in order of their place
                       values. The value of any digit in a number can be determined by that digit, its position in the number, and the base
                       of the number system.



                 Number system is a way of denoting numbers using digits or symbols. It also follows a definite set of rules to denote
                 the actual value. The value of any number depends on three factors, which are as follows:
                 •  digits or numerals
                 •  position of the digits
                 •  the base of the number system





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