To use Hexadecimal Calculator, enter the values in the input boxes below and click on the Calculate button.
The numeral system is the way we write and calculate numbers using symbols (digits), hence, the need for Hex Calculator. Depending on how we determine the value of a number from some notation, we distinguish between positional (=the value of each digit given by its position in a sequence of symbols; currently the most widely used) and non-positional number systems.
Hexadecimal (Hex) number system belongs to the positional systems; the base is, as the name implies, 16. It is the most used in computer science - it is used to write values of, e.g., registers and variables, and the device's Hex Calculator speeds up this process. This article about our hexadecimal calculator will give you an overview of the hexadecimal system. Here, you will also learn how arithmetic operations (Hex Calculator-calculation) are performed in the Hexadecimal numbering system. So, let us get started by answering the famous question: "what is a hex number? "
The hexadecimal number system, often shortened to "HEX," is a number system consisting of 16 symbols (base 16). The standard number system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses decimal numbers and six additional symbols, and our Hex Calculator allows you to perform the arithmetic operation you want in this system. There are no number symbols that represent values greater than nine, so letters taken from the English alphabet are used, specifically A, B, C, D, E, and F. The hexadecimal system A = decimal, and hexadecimal F = decimal 15.
More about Hexadecimal Calculator!
People mostly use the decimal system. This is probably because people have ten fingers on their hands, and instead of using a Hex Calculator, they use academic calculators from brands like Casio or Texas instruments, for example. On the other hand, computers only have off and on, called a binary digit. A Binary system is just a string of ones and zeros: 11011110, for example. For convenience (universality, efficiency), computer science Engineers tend to group bits together for the Hex Calculator and computer software. In earlier times, such as the 1960s, they would group three (03) bits at a time. It is important to note that only large decimal numbers are grouped in threes. An example may be the number 123.456,789.
The need for Efficiency.
As computers needs are growing every hour, day, year, etc., it became more convenient to group the bits by four instead of three, hence, the use of the hexadecimal system and Hex Calculator. Indeed, this doubles the numbers the symbol would represent; it could have 16 values instead of eight. Hexadecimal = 6 and decimal = 10, so it is called hexadecimal. In the computer science's jargon, the four bits form a nibble (sometimes spelled nybble). Two nibbles make up a byte (8 bits).
About Hexadecimal Calculator: Most computer operations use a byte or multiple of a byte (16, 24, 32, 64, etc.). To avoid confusion with the binary, octal, decimal, or other numbering systems, hexadecimal numbers are frequently written with "h" after or "0x" before the number. For example, 63h and 0x63 represent 63 hexadecimal numbers. Thanks to our Hex Calculator, you don't need to know all these complex concepts in order to add, multiply or divide many hex numbers.
The table below shows the equivalents of decimal, hex, and binary number (very handy when you don't want to use our Hex Calculator-manual calculation).
Decimal |
Hex |
Binary |
0 |
0 |
0 |
1 |
1 |
1 |
2 |
2 |
10 |
3 |
3 |
11 |
5 |
5 |
101 |
10 |
A |
1010 |
11 |
B |
1011 |
12 |
C |
1100 |
13 |
D |
1101 |
14 |
E |
1110 |
15 |
F |
1111 |
50 |
32 |
110010 |
63 |
3F |
111111 |
100 |
64 |
1100100 |
Hex Calculator: Where and why is hexadecimal used?
Most error codes and other values used inside a computer are represented in hexadecimal format. For example, error codes called STOP codes, which are displayed on a blue screen when the computer crashes, are expressed in hexadecimal format-I am curious to know if the Hex Calculator is used here.
Programmers like to use hexadecimal numbers compared to the others because their values are shorter than if they were displayed in decimal and much shorter than in binary, which uses only 0 and 1; this simplifies the workload of the computers or servers' Hex Calculator. Let us take the example of the hexadecimal number: F4240; when written in using other systems (binary, decimal), it is equivalent to 1111 0100 0010 0100 0000 in binary and 1,000,000 in decimal and. More about the uses of Hexadecimal numbers, hence, Hex Calculator in the next paragraph.
Additionally, the hexadecimal system- Hexadecimal Calculator- is used to express a specific color in the HTML color coding. For example, a web designer will use the hexadecimal value FFA500 to define the color orange.
Like the octal system, the hexadecimal system shortens the storage of binary data. Each number system has a number of digits equal to the base of the system. As we aid in the previous sections of this article about Hex Calculator, the base of this system is the number 16, which is 2 to the power of 4 - (24). One character in the 16 system will replace four characters in the binary system. Let's check it on an example:
Let's convert the number 12 from decimal to the binary system.
The number 12(10) = 1100(2)
We have proved that we need 4 characters to write it. More About Hex Calculator: To convert a number from binary (2) to hexadecimal (16), you need to divide the number by four bits (4 characters), remembering that you start from the right! If the last digits in the grouped number have less than four characters, we need to fill them with zeros. Then convert each resulting 4 digits of the binary system to the corresponding 1 digit of the hexadecimal system. Remember: you don't have to know all these details if computer science is not your field; With the help of our Hex Calculator and the other software on our site, you do this conversion in seconds.
Using the previous table, it is much easier to do a Binary to Hex conversion. We will break down the main steps-the simple method.
Step 1: take 4-bit packets.
This first step is very easy, you just have to take always groups of 4 bits. Here are some concrete examples to explain what it means:
Example 1:
It means, when you have less than 4 bits, then you add zeros in front to reach the number of 4 bits requested. I am sure you are already in love with this article about Hex Calculator. Let us move to the next step.
Step 2: refer to the binary-hexadecimal conversion table above.
The second step is easier than the first one. Just take each grouping of 4 bits and make the correspondence between binary and decimal. Here are some illustrations of what you will get:
Example 1:
Remember to do the first step when there are less than 4 bits.
Like any number system, the hexadecimal system also has operations on numbers. However, operations on hexadecimal numbers are not used very often. In the following section of this article about Hex Calculator, we will cover the addition, division, multiplication, and subtraction of Hexadecimal numbers.
How to do hex addition?
Decimal addition has the same rules for hexadecimal addition, except for the addition of the numbers A, B, and C. If these numbers are not stored in memory, it may be useful to have the equivalent decimal values A through F on hand. Let us move to the next arithmetic operation of our blog post about Hex Calculator.
Hex Calculator: Hexadecimal subtraction
Hexadecimal subtraction can be performed in the same way as hex addition. This is accomplished by performing an operation when converting between decimal and hexadecimal values. Borrowing is the most important difference between decimal and hexadecimal subtraction. A "1" in hexadecimal is 16 decimal places, not 10 decimal places in borrowing. Thanks to our free Hex Calculator, you don't have to know all these rules. This is because the column that is borrowed is 16 times larger than the borrowing column.
How to multiply hexadecimal values?
Multiplication in the hexadecimal system can be challenging because of the difficulty in converting between decimal (hexadecimal) and decimal (decimal) operations. The digits are generally larger, so it requires more effort. For our Hex Calculator, it is a very simple operation, and you can do it in less than 60 seconds. It may be useful to have a table of hexadecimal multipliers. Manual conversions between decimal (hexadecimal) numbers will be needed for each step.
Hex Calculator -> Division of Hex Number.
Division in hex is exactly like long division in decimal. However, multiplication, as well as subtraction, is done in hex. You can also convert decimal places to perform your division and then return after the conversion is complete.