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This logical representation of numbers is the basis of all mathematical and algebraic calculations. A number system is
generally categorised depending on its base. The four commonly used number systems are:
• Decimal number system
• Binary number system
• Octal number system
• Hexadecimal number system
1.1.1 Decimal Number System
Deca means ten and as the name suggests, the decimal number system is a positional value-based system with base
10 in which the rightmost digit has the lowest position and is called the Least Significant Digit (LSD). The leftmost
digit has the highest position and is known as the Most Significant Digit or MSD. The integer parts are represented
by a positive power of 10, while the decimal parts are represented by a negative power of 10.
Definition
Decimal number system has base 10. The numerals or digits of Decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Say any number 123456.0789 is represented as,
10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4
1 2 3 4 5 6 . 0 7 8 9
Decimal Odometer
We have all seen an instrument called an odometer in automobiles. It is used to measure the distance travelled by the
vehicle. The decimal odometer contains a set of wheels which have digits 0 to 9 written on them.
Thousand Hundred Ten Unit Fractional part
0 0 0 0 0
A new vehicle has an odometer reading 00000. When a car starts moving, the rightmost tab
keeps changing from 0, 1, 2 till 9. After the rightmost wheel has completed one rotation, the
fractional tab is reset to 0 and 1 is carried to the units tab. When the unit wheel completes
one rotation, the tens tab changes to 1 and the reading shows 00010. This odometer can
have a maximum value 99999.
1.1.2 Binary Number System
With the invention of digital devices like computers, another branch of mathematics called Boolean Algebra was
developed, which uses binary numbers containing only two digits 0 and 1. Binary number system is the base for all
modern electronic and computing devices.
Definition
Binary number system has base 2 and digits 0 and 1. Like the decimal number system, it is also a positional
value-based system where each digit has its weight denoted as a power of 2.
16 Touchpad Computer Science (Ver. 3.0)-XI
