The decimal number system is something we all have studied in school. We have learned to read and write numbers in this system, understand it and use it on a daily basis. In this article, we will tell you how to convert the decimal numbers into another base in a variety of natural ways. This can be useful when expressing values that are difficult to express in decimal notation. One such example, for example, is binary representation of fractions and percentages (not discussed here).
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What is Hexadecimal?
Hexadecimal (Hexadecimal), or HEX for short, is a base 16 number system consisting of 16 unique symbols and used to represent a piece of data. These 16 numbers contain the numbers 0-1-2-3-4-5-6-7-8-9 and the letters A, B, C, D, E, F. Decimal, or hexadecimal, which is similar to the decimal number system that we use in our daily life, is a number system that is often used in the fields of information technology.
Have you ever noticed that most of the error codes used in computers appear as hexadecimal? Error codes, status codes, stop errors, and blue screen errors are constantly displayed by error codes from the hexadecimal unit. This is because computer programmers program error codes to be hexadecimal. Hexadecimal data is written shorter than the value it represents. So in a few numbers, they can actually convey a much deeper message to us. Computer programmers use hexadecimal because hexadecimal is shorter when compared to Binary or Decimal.
Let’s explain with a simple example; A hexadecimal value of F4240 can be written as 1,000,000 decimal and Binary code as 1111 0100 0010 0100 0000. Therefore, hexadecimal data can present the value it represents to us, even though it is written shorter.
Another area where hexadecimal is widely used is in HTML color codes, which help symbolize exactly one color. A web designer will render the color red with the hexadecimal code FF0000. This code is parsed as FF,00.00 and represents how many red, green and blue colors will use each digit.
Hexadecimal values can fit up to 255 values into two digits of data. Since HTML color codes consist of three sets of values, it is possible to easily express over 16 million color ranges using HEX (255 x 255 x 255). Considering number systems such as decimal, hexadecimal offers us the advantage of time, size and space in this respect. Although the binary code system is easier to use in many ways, hexadecimal values can be easily read and understood by humans.
What is Decimal?
Decimal is the decimal number system used in the computer content system. Using Decimal, any content can be encoded according to the decimal system and this encoding can be read and understood by humans. Those who will work in the field of computer science should have a good grasp of the relationship of Decimal with Binary, Octal and hexadecimal in terms of understanding the logic.
In the decimal number system, the digits 0-1-2-3-4-5-6-7-8-9 are used, unlike the 0 and 1 used in Binary. Since the sum of the digits used, including 0, consists of 10, this system is called the decimal number system. Although most modern computers count Binary, there are still computers that work by counting (Decimal Computers). Charles Babbage’s Analytical Engine was designed using the decimal system. ENIAC and IBM 650, which we can accept from the first computer examples, also use the decimal number system.
The decimal number system in mathematics is as old as humanity. According to rumors, the reason why this system has a 10-computing model is that people calculate using their 10 fingers when they do not have hard-to-reach tools such as paper and pencil. In ancient times, Greek mathematicians tried to calculate the width of the universe using the decimal number system, while Chinese mathematicians prepared their abacuses according to the decimal system.
How to Convert Hex To Decimal
Microprocessors use Binary (2 decimal), Decimal (10) and Hexadecimal (16 decimal) number systems. The binary number system is a number system that microcontrollers can understand. The decimal number system is the decimal number system we have seen since elementary school. The hexadecimal number system is a system that helps us to easily understand our binary number system. However, the programmer needs to know the relationship between these three number systems very well, because in some operations he will need to make the best conversions between each other.
In the hexadecimal number system, numbers 0 to 9 represent numbers 0 to 9, and letters A to F represent numbers 10, 11, 12, 13, 14, and 15, respectively.
For example, if we want to calculate the decimal equivalent of the hexadecimal number 2AF3
We can find (2 × 16³) + (10 × 16²) + (15 × 16¹) + (3 × 16⁰ = 10995…
If we want to write the hexadecimal number as Binary, it will be sufficient to write the groups of 4 corresponding to each value side by side.