Page 17 - ComputerScience_Class_11

SyStem of NumeratioN

1

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 the prehistoric
age. Initially, counting was done using pebbles, sticks, bones, etc. where each stick, pebble or bone represented one
object. The tally stick counting method was also practised by making marks or cutting notches into pieces of wood or
even tying a knot in string. With the advancement of human civilisation, the requirement to represent larger numbers
increased. The need for better representations led to the 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
system was established. The positional system was further modified in the Hindu-Arabic number system, which was
developed during the 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

System of Numeration 15