In General when we are talking about the number of people in a bus, also number of people waiting outside a booking window, also waiting number of a person in a reservation schedule. In these examples we are just taking about numbers or quantifying them.

So we can say that “A number system defines a set of values used to represent a quantity.”

A **number** is a mathematical object used in counting and measuring.

In general, We have two types of number system

- Non-positional
- Positional

In mathematics, the definition of number has been extended over the years to include such numbers as

- Rational numbers,
- Irrational numbers, and
- Complex numbers.
- So, the study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work.

In reference to computer architecture, number systems are very important to understand because the design and organization of a computer is dependent upon the number system. This will give us an insight of how computers manipulate and store numbers.

So we will discuss non-positional and positional number system in this lecture.

## Non-positional Number System

In this system, each symbol represent the same value regardless of its position in the number and the symbols are simply added to find out the value of a particular number e.g. we have symbols such that I for 1, II for 2 ……III for 3 etc.

## Positional Number System

Those numbers in which each digit has its importance, like 234 read as two hundred and thirty four. Because in this number each digit has its importance. We read in primary education about One’s(इकाई), Tens(दहाई) and Hundreds(सैंकड़ा), these are the different positional values for decimal number system, which is used in our daily life. The value of each digit in this number is determined by

- The digit itself
- The position of the digit in the number.
- The base or radix of the number system.
- Base or Radix

*Now, What do you mean by base*? The base of a number system is defined as the number of different symbols used to represent numbers in the system. The decimal system uses ten symbols 0,1,2,3….9. and its base is ten(10). E.g. a decimal number 234 can be represented as

2x(10)2 + 3x(10)1 + 4(10)0

2×100 +3×10 +4×1

200 + 30 + 4 = 234

Hence, Left most digit(2) value is 200 and Right most digit(4) value is 4. So Left most digit is known as Most Significant Digit(MSD) and Right most digit is known as Least Significant Digit(LSD).

## Various types of Positional Number Systems

The various number systems is essential for understanding of computers so we begin with the number systems. The various positional number systems are

- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System

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