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Hex Calculator

Hex Calculator

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Use this best hex calculator to perform various arithmetic operations on a couple of hexadecimal numbers. Not only this, but this free hex converter will also let you convert the given base 16 numbers into its corresponding decimal, octal, and binary notations.

So what do you think about moving ahead and understanding the concept of hexadecimal system? Interested enough?

Let’s move on!

What Is a Hexadecimal System?

In the light of digital logic design study:

“The hexadecimal system is such a logical method that considers the base of number 16 just like that of binary, decimal, and octal, which use the base of 2, 10, and 8, respectively.”

Here below, we will be throwing a light on the hexadecimal system in particular. So be with us and keep getting more!

Operations on Hexadecimal Numbers:

If you are in continuous touch with us till now, then it’s great. Keep scrolling to know how you could apply mathematical operations on hex numbers.

Hexadecimal Addition:

The addition of a couple or more hex numbers is just like those of other systems that are octal, binary, and decimal. What we need to consider here is that the base is 16 just. You can also use this online hex addition calculator to speed up your calculations accordingly.

Example:

Suppose we have the following hex numbers to be added:

$$ (2BC)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A56\right)_{16} $$

Solution:

  2 B C

+A 5 6


  D 1 3

Detailed Calculations:

The given numbers are:

$$ \left(2BC\right)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A56\right)_{16} $$

Adding hexadecimal numerals:

$$ \left(2BC\right)_{16} + \left(A56\right)_{16} $$

$$ C + 6 = 12 + 6 = 18 $$

As the number 18 is greater than 16, we will divide it by 16 to get the carry and the remainder:

$$ \frac{18}{16} $$

Remainder = 2

Carry = 1

The remainder 2 will be written below the line and the carry will be added to the next column which is:

$$ carry 1 + B + 5 = 1 + 11 + 5 $$

$$ = 16 $$

As we get exactly 16, so we will again divide it by 16 to get the next remainder and carry.

$$ \frac{16}{16} $$

Remainder = 0

Carry = 1

This carry will be added to the third and last column which is the most left one

$$ carry 1 + 2 + A = 1 +2 + 10 $$

$$ = 13 $$

As this number is smaller than the hex base number that is 16, so it will be written as it is in the answer as D.

Final answer:

$$ \left(2BC\right)_{16} + \left(A56\right)_{16} = \left(D12\right)_{16} $$

For verification, you can also let this hexadecimal addition calculator do that for you in a blink of an eye.

Hexadecimal Subtraction:

Hex subtraction is just like that of the decimal addition. But the only thing that differs here is that you need to consider the carry 1 as 16, which is 10 in the case of the decimal system. Here to avoid confusion and take control over the calculations, you can use this free hex calculator for the sake of instant and accurate outputs.

Example:

Let’s subtract a couple hexadecimal numbers given below:

$$ (BA)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A3\right)_{16} $$

Solution:

  B A

– A 3


  1 7

Detailed Calculations:

As the given numbers are:

$$ (BA)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A3\right)_{16} $$

Subtracting these hex numbers:

$$ (BA)_{16} – \left(A3\right)_{16} $$

$$ A – 3 = 10 – 3 = 7 $$

Remainder = 7

Carry = 0

Moving to the next column:

$$ B – A $$

$$ = 1 $$

Final Answer:

$$ (BA)_{16} – \left(A3\right)_{16} = \left(17\right)_{16} $$

To speed up your computations, you can let our free hex subtraction calculator do that for you in a blink of moments. What are your thoughts on it?

Hexadecimal Multiplication:

Hex multiplication can be tricky enough but this free hex calculator online will let you do calculations in a matter of seconds. Anyways, as manual steps are also important to understand, so let’s move on understanding them as below:

Example:

Multiply the following hexadecimal numerals:

$$ (BA)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A3\right)_{16} $$

Solution:

   1 D

 * 2 3


 1 5 7

3 A 0


4 F 7

Detailed Calculations:

Here the given numbers are:

$$ (BA)_{16} \hspace{0.25in}and \hspace{0.25in} \left(A3\right)_{16} $$

Multiplying these numbers:

$$ (BA)_{16} * \left(A3\right)_{16} $$

$$ 3 * D = 39 $$

As 39 is greater than 16, so we will divide it by 16 to get carry and the remainder:

Remainder = 7

Carry = 2

This carry will be added to the next column as follows:

$$ 3 * 1 = 3 + carry 2 = 5 $$

Now the second number 2 will be multiplied with the upper row:

$$ 2 * D = 26 $$

As 26 is higher than 16, so we will divide it by 16 to get remainder and carry as follows:

Remainder = 10 = A

Carry = 1

Now we will add this carry in the next column as:

$$ 2 * 1 = 2 + 1 = 3 $$

Now adding all the numbers:

$$ 7 + 0 = 7 $$

$$ 5 + A = 15 = F $$

$$ 1 + 3 = 4 $$

Final Answer:

$$ (BA)_{16} * \left(A3\right)_{16} = \left(4F7\right)_{16} $$

Hexadecimal Division:

You can perform hex division by three ways:

  • Directly dividing the hex numbers as they are
  • Converting hex numbers into decimal numbers, dividing, and then converting back decimal numerals to hexadecimal numerals
  • By using our fast hex calculator online which is the best way considered so far

Converting To and Fro From Hex Numerals:

As you know that both calculation and conversion are two separate methods. When it comes to conversion, the hex numbers do not alter at all but only change their system format. Our free hexadecimal calculator also goes for such conversion to make your understanding more clear and precise. But if you want to learn manual methods, you may continue reading!

Hexadecimal to Decimal Conversion:

It’s not a great deal to convert any hex number to its corresponding decimal notation. What you need to do is to consider the following key points in your mind:

  • Each hex number must be converted to decimal number
  • After this is done, you need to multiply each number with 16 separately and add all of them
  • At the end, the number you will get would be in decimal system
Example:

Convert the following hexadecimal number to its decimal number format:

$$ \left(A 6 9\right)_{16} = \left(?\right)_{10} $$

Solution:

$$ \left(A 6 9\right)_{16} = \left(A * 16^{2}\right) + \left(6 * 16^{1}\right) + \left(9 * 16^{0}\right) $$

$$ \left(A 6 9\right)_{16} = \left(10 * 16^{2}\right) + \left(6 * 16^{1}\right) + \left(9 * 16^{0}\right) $$

$$ \left(A 6 9\right)_{16} = \left(10 * 16^{2}\right) + \left(6 * 16^{1}\right) + \left(9 * 16^{0}\right) $$

$$ \left(A 6 9\right)_{16} = 10*256 + 96 + 9 $$

$$ \left(A 6 9\right)_{16} = \left(2665\right)_{10} $$

If you wish to avoid these complex computations, you can use our online hex to decimal converter for the sake of accurate conversions.

Decimal To Hexadecimal Conversion:

This conversion may be a little tough to carry out but do not worry. This is because our online hex calculator online will assist you a lot in determining the hex form of any decimal numeral. For manual calculations, please keep going through the example below:

Example:

Convert the given decimal number to its equivalent hex number system:

$$ \left(266\right)_{10} = \left(?\right)_{16} $$

Solution:

Here we have :

$$ 266/16 = Remainder 10 & Quotient 16 $$

The remainder will be written as hexadecimal notation with its related hex alphabet if present.

$$ \left(266\right)_{10} = \left(10A\right)_{16} $$

Hexadecimal to Binary Conversion:

For hex to binary conversion, we need to follow the table below:

Hexadecimal

Decimal
0

0000

1

0001
2

0010

3

0011
4

0100

5

0101
6

0110

7

0111
8

1000

9

1001
A

1010

B

1011
C

1100

D

1101
E

1110

F

1111

Binary to Hexadecimal Conversion:

For this conversion, you need to keep in mind the following couple of steps:

  • First, you need to start from right and divide the binary number into sets, each containing 4 digits
  • After you do that, follow the table as mentioned above to write the hex numeral against the given binary number

How Hex Calculator Works?

This hex value finder will not only let you perform various operations on hexadecimal numbers but also convert them to various other logical notations. We understand it seems a little bit tricky, but do not worry at all. Okay let’s move on having a look at its operation!

Input:

  • From the top drop-down list, make a selection whether you want to apply any operation on the numbers or convert the hexadecimal number into other notations
  • After you make a selection, fix the numbers in their designated positions
  • At last, hit the calculate button and there you go

Output:

The best hex converter will do the following operations and conversions on the given numbers:

  • Determine the results of the operation applied on the numbers (Addition, Subtraction, Multiplication, and Division)
  • Also convert the hexadecimal number into its corresponding notations (Binary, Decimal, and Octal)

FAQ’s:

Why hexadecimal system is used?

Hexadecimal numbers are commonly used by software developers and system designers because they provide a human-friendly representation of binary-coded data. Because of this importance, these numbers are used in logical reasoning to run fast computers.

What is a 64 digit hexadecimal number?

The maximum value of a 64-bit (or 8-byte) hex number is 18,446,744,073,709,551,615. You can also verify this by using our free hex calculator online.

What is the difference between ASCII and hexadecimal?

The American Standard Code for Information Interchange is abbreviated as ASCII. It has a decimal range of 0 to 255 and a hexadecimal range of 00 to FF. On the other hand, the hexadecimal system is a logical method that takes the base of 16 into account.

What is FFFF in decimal?

The decimal value of FFFF in hexadecimal notation is 65535. You can also verify it by using the hex calculator online in a couple of seconds.

Conclusion:

The fundamental benefit of a hexadecimal number is that it is relatively compact, and because it uses a base of 16, the number of digits necessary to express a positive integer is usually less than in binary or decimal. Converting from hexadecimal and binary numbers is also simple and quick. And to make the process quicker, our free hex calculator will let you do so without any hurdle.

References:

From the source of Wikipedia:  Hexadecimal, Representation, Distinguishing from the decimal, digital representations, Hexadecimal exponential notation, Binary conversion, Elementary arithmetic

From the source of khan academy: Hexadecimal numbers, Converting binary to hexadecimal, Patterns 

From the source of lumen learning: Binary, Octal, Hexadecimal