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Welcome to decimal to hex, our website which explains the decimal to hexadecimal conversion to you.
The decimal numeral system is also referred to as dec, base 10 and denary, whereas the hexadecimal writing system for numbers is also called hex or base 16.
If you have been wondering about how to convert decimal to hexadecimal, or if you have been looking for how to convert dec to hex, then you’re perfectly right here. 🙂
We have put the converter right below.
About our Decimal to Hex Converter
Our decimal to hex converter in the above section is straightforward: Insert your value in decimal notation.
The calculation is done automatically, without the need to press a button.
If you fill in the bottom field, then the conversion changes to hex to dec.
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BTW: Our frequent conversions include:
Next, you can find more information about the numeral system under consideration; how to convert decimal to hexadecimal is explained further below.
Dec to Hex
In the mathematical operation called exponentiation bn b is the base and n is the exponent.
The decimal system is a positional numeral system with a base b of 10, and the exponents are 0, 1, 2, … n, according to the (n-1)th position of the digit, starting the count with one.
100 = 1, 101 = 10, 102 = 100, etc.
The decimal notation uses the symbols zero to nine.
If it is clear which base is meant, such as in daily use of counting, the base is omitted.
When a base is explicitly stated, then it is usually put in subscript as can be seen in the case below.
For example, 432910 denotes 4 x 1000 + 3 x 100 + 2 x 10 + 9 x 1
The hexadecimal system a positional numeral system with the base 16 and the exponents are 0, 1, 2, … n, according to the (n-1)th position of the digit, assuming one is the first number.
160 = 1, 161 = 16, 162 = 256, 163 = 4096 and so forth.
The hex system of numeration uses the symbols 0–9 and a–f.
The letters a–f or A-F denote the numbers ten to fifteen.
For example, 10e916 denotes 1 x 4096 + 0 x 256 + 14 x 16 + 9 x 1, that is 432910.
The table below translates between the two notations:
How to Convert Decimal to Hexadecimal?
Here we are going to show you how to conduct the operation using the remainder method, which can be broken down to this four steps:
- Divide the decimal by 16, record the integer part of the result as new quotient
- Write down the remainder of the result in hexadecimal notation using our table above
- Proceed the two steps above with the quotient until the result is 0
- Build the result as a sequence of the hex remainders from right to left, from top to bottom.
Below is the example for 432910:
|4329||16||270||9 (4329 – 16 x 270)||9|
|270||16||16||14 (270 – 16 x 16)||e|
|16||16||1||0 (16 – 1 x 16)||0|
|1||16||0||1 (1 – 0 x 16)||1|
432910 = 10e916
Proof: 1 x 163 + 0 x 162 + 14 x 161 + 9 x 160 = 4096 + 0 + 224 + 9 = 4329.
Below is another example, 777710:
|7777||16||486||1 (7777 – 16 x 486)||1|
|486||16||30||6 (486 – 16 x 30)||6|
|30||16||1||14 (30 – 1 x 16)||e|
|1||16||0||1 (1 – 0 x 16)||1|
777710 = 1e6116
Proof: 1 x 163 + 14 x 162 + 6 x 161 + 1 x 160 = 4096 + 3584 + 96 + 1 = 4329.
If you need more examples, then you may want to check out our frequent conversions located below our calculator.
Every posts contains the math in full detail.
As a side note: In programming it is common to write a base 16 number with the 0x prefix.
Therefore, for instance, 1e6116 = 0x1e61.
How to Convert a Decimal Number with Fractional Part into Hexadecimal?
For this, we split the number into a whole number part and a decimal part, then combine the results. Thus, in this section we only discuss the fractional part.
- Multiply the decimal number by 16 and write down the integer part in hex notation
- Repeat the first step until the fractional part equals zero
- Build the result as a sequence of the hex remainders from right to left, from top to bottom, following the decimal separator
Observe that, depending on the input, the process might take an endless number of iterations, thus you may want to stop after n digits and use the result as an approximation.
Here’s an example of how to convert dec to hex with digits, the number is 0.00390625:
|Decimal||Multiplicator||Product||Integer Part||Fractional Part|
0.0039062510 = 0.0116
Proof: 0 x 1/16 + 1/(16×16) = 0 + 1/256 = 1 /256 = 0.0039062510
Ahead is the summary of our information regarding base 10 to base 16.
Convert Decimal to Hex
You have reached the concluding section of our dec hex article. The frequently asked questions in the context our visitors have, include:
- How to convert denary to hexadecimal?
- How to calculate decimal to hexadecimal?
- How to convert from base 10 to base 16?
Taking into account our information, you should now be versed to conduct a decimal to hex conversion using our method and to answer these FAQs, too.
In addition, you can always check your result using our decimal to hex converter and ask us a question by filling in the comment section at the end of this page.
Alternatively, send us an email with the subject line convert decimal to hex.
This image sums denary to hexadecimal up:
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