Hexadecimal number system
The hexadecimal (base 16) number system
is a positional number system as are the decimal number system and the binary number system. Recall that in any positional number system, regardless of the base, the highest numerical symbol always has a value of one less than the base. Furthermore, one and only one symbol must ever be used to represent a value in any position of the number. |
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Objectives:
1- Understand the concept of number systems.
2- Find the number of digits needed in each system to represent a particular value.
3-Describe the decimal, binary, hexadecimal.
4-convert a hexadecimal number to decimal number.
5-Distinguish between non-positional and positional number systems.
2- Find the number of digits needed in each system to represent a particular value.
3-Describe the decimal, binary, hexadecimal.
4-convert a hexadecimal number to decimal number.
5-Distinguish between non-positional and positional number systems.
Converting a Hexadecimal Number to a Decimal Number
We can use the same method that we used to convert binary numbers and octal numbers to decimal numbers to convert a hexadecimal number to a decimal number, keeping in mind that we are now dealing with base 16. From right to left, we multiply each digit of the hexadecimal number by the value of 16 raised to successive powers, starting with the zero power, then sum the results of the multiplications. Remember that if one of the digits of the hexadecimal number happens to be a letter A through F, then the corresponding value of 10 through 15 must be used in the multiplication.
A number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16and (52)8both refer to the same quantity, (42)10,but their representations are different.
Several number systems have been used in the past and can be categorized into two groups: positional
and non-positional systems. Our main goal is to discuss the positional number systems, but we also give
examples of non-positional systems.
A number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16and (52)8both refer to the same quantity, (42)10,but their representations are different.
Several number systems have been used in the past and can be categorized into two groups: positional
and non-positional systems. Our main goal is to discuss the positional number systems, but we also give
examples of non-positional systems.
Here are the basic '16' base number in hexadecimal number chart
![Picture](/uploads/1/3/6/2/13622043/3914714.jpg?1349852394)
Now go to the podcast to learn more about hexadecimal number conversion.