Conversion of octal numbers to hexadecimal

Converting octal numbers to hexadecimal is mediated by binary system of numbers like this example :

Directly converting from binary system to octal number system

Converting from binary system to octal number system is done in the same way as converting binary system to hexadecimal system of numbers
Binary digits of the number are grouped into groups of 3 digits.

Example:

Direct conversion from hexadecimal to binary

Passing directly from hexadecimal system to binary system of numbers is done by finding for each digit hexadecimal number four bit binary equivalent

Example: 

Directly converting from Binary to Hexadecimal

For the conversion of a numeral system to another system, can be used as an intermediary decimal system of numbers.
• Many complex calculations
• in practice used direct switching between numeral systems.


Converting from binary system to hexadecimal system is on two steps :
Binary number is divided into groups of 4 digits starting from the right.
Each group has an equivalent hexadecimal number

Example : 

Converting from hexadecimal to decimal numbers

As octal and binary system hexadecimal number system conversion can be done using the formula

For the base numerical system will be B = 16

Example :

Hexadecimal numeral system

Hexadecimal system, the numbers are written using 16 different digits:

0 1 2 3 4 5 6 7 8 9 A B C D E F

Since hexadecimal numbering system used 16 different digits, the basis of this numerical system is B = 16.


Transformation procedure hexadecimal floating point numbers in the same as the previous systems.
• divide the base 16

Example:

Converting from octal to decimal numbers

As binary system, octal system conversion numbers can be done using the formula :

On the base of the numeral system will be B = 8

Example:

Octal numbers system

Octal number system base is B = 8, because the numbers in the numerical system written using 8 different digits:

0, 1, 2, 3, 4, 5, 6, 7

The way to convert decimal numbers into octal system numbers is the same as that given for the binary system but here is multiplied or divided by the base B = 8.

Example:

Converting binary numbers to decimal

To find the decimal equivalent of binary numbers can be used formula

On the basis of the numbering system will be B = 2

Example :

Converting decimal numbers to binary numbers

Binary equivalent of a decimal number is obtained by dividing the number decimal successfully with number 2, as is the base B of the numerical system.
In each division, the remnant described in a column, and the division continues until the number is divided is not zero.

Example : 

Shortly for the Binary numbers system

Digital system to which the numbers are written using only the digits 0 and 1 is called the binary number system.
Binary numbers base is B = 2.
Numbering system that is used by computers for all calculations
An example of binary string :
11010111011

Converting numbers

The base of the decimal system of numbers is B = 10, because the numbers in the numerical system written using 10 different digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Any number X.Y numerical system based B can be written as a floating point number N through with (m + n) elements, like this:

Table of Numeral Systems

Numeral Systems

Present numerical systems arranged piles of symbols (digits), who defined four basic mathematical operations:
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adding (+)
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subtraction (-)
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multiplication (·)
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division (/).
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The number of different figures which are used during the writing of numbers in a digital system, is the basis of the numerical system.