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Before you convert a decimal to ahexadecimal and a hexadecimal to a decimal you must know what decimal bits and hex bits are.
51 rows How to convert from hex to decimal. A regular decimal number is the sum of the digits. How to convert from decimal to hex Conversion steps: Divide the number by 16. Get the integer quotient for the next iteration. Get the remainder for the hex digit.
What Is a Decimal?
First, a decimal or hex bit in this tutorial represents a single number, digit, or letter. A decimal is also called base 10 and denary because it consists of ten numbers. These are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
A decimal is a number system and can be represented using a subscript of 10 (i.e. 23510 reads as two hundred and thirty-five base 10).
Decimals are the numbers we use in everyday counting. We mostly use the decimal number system because we have ten fingers. The number 10 is made by using a combination of two of these decimal numbers: 1 and 0 while a number like 209 is a combination of three decimal numbers: 2, 0, and 9.
There is no limit as to how many times the numbers can be reused, that's why it is often said that numbers are never ending.
What Is a Hexadecimal?
A hexadecimal, which is also called base 16 or 'hex' for short, is a representation of four binary bits and consists of sixteen numbers and letters. The numbers in a hex are the same as decimal numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The big difference between a hex and a decimal is that a hex also contains letters. These letters are: A, B, C, D, E, F.
A hex number can be represented using a subscript of 16 (i.e. 23516). These letters come after the decimals in ascending order. Therefore, the hexadecimal series looks like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. A hex can be considered a shorter version of a decimal. For example a large number in decimal form has a much smaller hex equivalent (using less hex bits to represent the decimal number). I will demonstrate this later.
Converting a Hexadecimal to a Decimal
Now, how do you convert a hex to a decimal and a decimal to a hex manually? First, you must know the letters in a hex all have decimal equivalents, as listed in the table below.
There are other number system table with more values for octals, hexes, decimals, and binaries, however the table below provides all that we need for this tutorial.
Hexadecimal to Decimal Table
0 | 2 | 4 | 6 | 8 | A | C | E | |
---|---|---|---|---|---|---|---|---|
Decimal | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
How Do You Convert From Hex to Decimal Manually?
To convert a hexadecimal to a decimal manually, you must start by multiplying the hex number by 16. Then, you raise it to a power of 0 and increase that power by 1 each time according to the hexadecimal number equivalent.
We start from the right of the hexadecimal number and go to the left when applying the powers. Each time you multiply a number by 16, the power of 16 increases.
When converting a C9 hexadecimal to a decimal your work should look something like this:
Example 1
9 = 9 * (16 ^ 0) = 9
C = 12 * (16 ^ 1) = 192
Then, we add the results.
192 + 9 = 20110 decimal
Review
- First, we converted all of our hex numbers to their decimal equivalents. C is equal to decimal 12 (refer to table above) and 9 is equal to decimal 9.
- Then, we multiplied the numbers 12 and 9 starting from the last number in the question by 16 and its power. Remember, the powers start from zero.
- Our first multiplication had a power of 0 and the second multiplication had a power of 1. If there was a third it would have had a power of 2.
- The (^) symbol represents 'raised to the power of.' Therefore, the first terms in brackets read, '16 to the power of 0.' This means that sixteen was multiplied by itself zero times. Anything raised to the power of zero is 1. Therefore, 9 was multiplied by one.
- In the second bracket, the term read, '16 to the power of 1.' A number raised to the power of one is equal to that number. Therefore 12 was multiplied by 16. When we multiplied these we got 192.
- We then added the results to get our decimal equivalent number, which was 201.
Example 2
In this example, we want to convert hex ABC to a decimal.
Remember that we raise the number 16 to 0 for the rightmost bit of the question. As we move across the numbers and letters, the power 16 is raised by one more than the previous bit. For example, if we had a number with 22 in the leftmost bit it would be multiplied by 16 to the power of 21.
C = 12 * (16 ^ 0) 12
B = 11 * (16 ^ 1) 176
A = 10 * (16 ^ 2) 2560
B = 11 * (16 ^ 1) 176
A = 10 * (16 ^ 2) 2560
Then, we add the results.
2560 + 176 + 12 = 274810 decimal
Test Yourself!
- Convert Hex AF, ACD, AB2 and FF to base 10
Answers are 17510, 276510, 273810, and 25510 respectively.
How Do You Convert From Decimal to Hexadecimal Manually?
To convert from decimal to hexadecimal you must divide the decimal number by 16 repeatedly. Then, write the last remainder you obtained in the hex equivalent column. If the remainder is more than nine, remember to change it to its hex letter equivalent. The answer is taken from the last remainder obtained. Refer to the diagram below as an example:
Example 1
Base Ten Number | Hex Equivalent |
---|---|
201 | X |
12 | 9 |
0 | C |
Thus, the answer is C9. As you can see, it contains less bits than its decimal equivalent, 201.
Review
- We divided our decimal number (base 10) by 16 to convert it to a hex equivalent (base 16).
- Our decimal number was 201. We divided this by 16 to get a value of 12 with a remainder of 9. The hex equivalent for 9 is 9 so no change was made.
- We then divided our previous answer, 12, by 16. We got a value of zero and a remainder of 12. We then converted 12 to hex. The hex equivalent of 12 is C (refer to the first table). We then wrote our answer from the last remainder we received to the first in the order from left to right.
Example 2
In this example, we want to convert decimal 3000 to a hexadecimal.
Base Ten Number | Hex Equivalent |
---|---|
3000 | X |
187 | 8 |
11 | B |
0 | B |
The answer is BB8 hexadecimal. Remember, we write the last remainder we received at the front of our answer
Test Yourself!
- Convert decimal 39554, 2856, 37 to base 16/Hex.
Answers are 9A82, B28, and 25 respectively.
Conclusion
For some, this may seem difficult at first. But rest assured that with a little practice, converting from a decimal to a hexadecimal and a hexadecimal to a decimal can be easily mastered.
It may help you to check your answers using a calculator, or to type your decimal value in the dec setting and then select 'hex' and press equal. Just do the opposite for hex to decimal. Another option is using a decimal to hexadecimal converter or a hexadecimal to decimal converter.
Still, I strongly recommend you learn how to convert these number systems manually before using the calculator. That way, you won't feel that you need to rely on a calculator.
How to Change a Hexadecimal to a Decimal Manually (Video)
How Do You Convert a Decimal to a Hexadecimal Using a Calculator? (Video)
How to Convert a Hexadecimal to a Decimal Manually (Video)
© 2010 easyguyevo
- YEAHI'M GONTAKE MY HORSE
- Thank you! I use https://www.bin-dec-hex.com/hex-to-decimal-convert.. to check the conversion result.
- It was a very helpful.Thanks for your easy way to understand these..
- Very good extremely clear in the instructions
- Thanks
- Convert decimal 201 to hexadecimalSolution:Integer Remainder201/16 =12. 912/16 = 0. 12 i.e. CHence decimal 201 = hex C9
- easy for me to understand , thank you
- I found some parts of this quite hard to understand, like the remainders and how to do it without a calculator. Please help me to understand, my maths isn't that good with division.
- Nice one!!! Its more fun in the Phillipines
- On example 2:Multiplication ResultC = 12 * (16 * 0) 1212 * (16 * 0 ) should equal zero.it should be:12 * (16 ^ 0) = 12
- On the last set of TRY THESE examplesI get 2857 = B29 .....NOT B28 or am I mistakenI have worked this back and again it is notB28 = 2856Please comment, Alex Lomas
- I've found most sites do not mention what you need to do with the remainder.201 / 16 = 12.5625To get the remainder of 9, like in the example, you need to take the remainder .5625 and multiply by 16.201 / 16 = 12.5625.5625 * 16 = 9Converting is a two step process, yet for some reason no one ever mentions this, hope this helps someone!
Active8 months ago
How do you convert between hexadecimal numbers and decimal numbers in C#?
Micha Wiedenmann11.2k1616 gold badges6969 silver badges107107 bronze badges
Andy McCluggageAndy McCluggageConvert From Hexadecimal To Decimal Calculator
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17 Answers
To convert from decimal to hex do..
To convert from hex to decimal do either..
or
Legends9,35777 gold badges5050 silver badges8989 bronze badges
Andy McCluggageAndy McCluggage20.9k1616 gold badges5353 silver badges6666 bronze badges
Jonathan RuppJonathan Rupp13.9k22 gold badges3939 silver badges5555 bronze badges
Burbank condensed bold font free. It looks like you can say
to get the decimal from hexdecimal.
The other way around is:
Peter Mortensen14.5k1919 gold badges8989 silver badges118118 bronze badges
Jesper Blad JensenJesper Blad Jensen
If you want maximum performance when doing conversion from hex to decimal number, you can use the approach with pre-populated table of hex-to-decimal values.
Here is the code that illustrates that idea. My performance tests showed that it can be 20%-40% faster than Convert.ToInt32(..):
Peter Mortensen14.5k1919 gold badges8989 silver badges118118 bronze badges
Vadym StetsiakVadym Stetsiak
Conversion From Hex To Decimal
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RobRob48133 gold badges77 silver badges2020 bronze badges
SklivvzSklivvz24.8k2424 gold badges103103 silver badges158158 bronze badges
Ecstatic CoderEcstatic Coder
This is not really easiest way but this source code enable you to right any types of octal number i.e 23.214, 23 and 0.512 and so on. Hope this will help you.
OmairOmair
Hex to Decimal Conversion
Decimal to Hex Conversion
user7925882user7925882
Try using BigNumber in C# - Represents an arbitrarily large signed integer.
Program
Output
Possible Exceptions,
ArgumentNullException - value is null.
FormatException - value is not in the correct format.
Conclusion
You can convert string and store a value in BigNumber without constraints about the size of the number unless the string is empty and non-analphabets
Convert From Hexadecimal To Decimal In Java
AravinAravin2,79811 gold badge2222 silver badges3737 bronze badges
Христо ПанайотовХристо Панайотов
If it's a really big hex string beyond the capacity of the normal integer:
For .NET 3.5, we can use BouncyCastle's BigInteger class:
.NET 4.0 has the BigInteger class.
Convert From Hex To Decimal Online
Peter Mortensen14.5k1919 gold badges8989 silver badges118118 bronze badges
msanjaymsanjay1,26622 gold badges1515 silver badges1818 bronze badges
My version is I think a little more understandable because my C# knowledge is not so high.I'm using this algorithm: http://easyguyevo.hubpages.com/hub/Convert-Hex-to-Decimal (The Example 2) Whql driver download.
Mihók BalázsMihók Balázs
sampathsrisConvert From Hex To Decimal Java
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JewelJewel
My solution is a bit like back to basics, but it works without using any built-in functions to convert between number systems.
Krisztián MolnárKrisztián Molnár
sametssamets
An extension method for converting a byte array into a hex representation. This pads each byte with leading zeros.
Luke PuplettLuke PuplettConvert From Hexadecimal To Decimal C#
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