Number Base

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In today’s Computer Science class, We will be discussing Number Base. We hope you enjoy the class!

 

 

 

A number base is the number of digits or a combination of digits that a system of counting uses to represent numbers.

A base can be any whole number greater than 0. The most used number system is the Decimal system, commonly known as base 10. The base of any number may be written beside the number, for example, 20₈ is read as 20 base 8.

The Decimal Numbers System:

These are numbers in everyday use. They are also called Denary numbers or numbers in base 10, which has the most important role in the development of science and technology. It has 10 symbols, these are: 0,1, 2, 3, 4, 5, 6, 7, 8, 9.

The position of every digit has a weight which is a power of 10. Each position in the decimal system is 10 times more significant than the previous position i.e. the numeric value of a decimal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products.

For example:

22= 2×10¹ + 2×10⁰

= 2×10 + 2×0 = 20 + 2

= 2210 or 22.

The Binary Number System:

The binary number system is a system that makes use of only the digits i.e. 0 and 1. The two digits are called binary digits or simply bits. It is referred to as a base 2 system. A computer can only understand the “on” and “off” state of a switch which is represented by 1 and 0 respectively. The binary number system uses positional notation but, in this case, each digit is multiplied by the appropriate power of two based on its position.

For example: convert 223₂ to base 10

223₂= 2×2² + 2×2¹ + 3×2⁰

= 2×4 + 2×2 + 3×1

= 8 + 4+3 = 1510

Octal Number System:

The octal system is the base eight system. This system uses digits 0 to 7 i.e. 8 digits, to represent a number and the numbers are as a base of 8.

For example: convert 22 from octal to decimal.

22₈= 2×8¹ + 2×8⁰

= 2×8 + 2×0 = 16 + 2

= 1810 or 18.

Hexadecimal Number System:

This is a system that uses 16 digits i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F; thus it is also known as the base 16 number system. Each digit position represents the power of 16. As the base is greater than 10, the number system is represented by letters (A-F) as seen above.

 

 

 

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about Conversion of Number base. We are very much eager to meet you there.

 

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