How to Convert Decimal to Hexadecimal

The hexadecimal system is the base sixteen system. That is, it uses 16 characters to represent single characters: add A, B, C, D, E and F to the usual ten digits. Converting from decimal to hexadecimal is more difficult than vice versa. Take the time to learn how to convert: once you understand its essence, you can easily avoid common mistakes and mistakes.

Table of Contents

Small number conversion

Decimal	0	first	2	3	4	5	6	7	8	9	ten	11	twelfth	13	14	15
Hexadecimal	0	first	2	3	4	5	6	7	8	9	A	REMOVE	OLD	EASY	E	F

Intuitive method

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Use this method if you are new to the hexadecimal system. This is the easier approach for most people. If you are comfortable with other bases, you can use the faster method below.

If you are completely new to the hexadecimal system, you should learn the basics.

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Write down to a power of 16. Each character in a hexadecimal number represents a value to a power of 16, just as each digit in a decimal number represents a power of 10. Powers of 16 will come in very handy when you need to convert:

16 ⁵ = 1,048,576
16 ⁴ = 65,536
16 ³ = 4.096
16 ² = 256
16 ¹ = 16
For decimals greater than 1,048,576, calculate a higher power of 16 and add to the list above.

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Find the largest power of 16 that matches your decimal. Write the decimal number to convert and compare with the list above. Find the largest power of 16 less than that number.

For example, with 495 , we will choose 256 from the list above.

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Divide the decimal by the chosen power value. Take only the integer part, ignore the decimal part of the quotient.

In the example problem, 495 ÷ 256 = 1.93… but we are only interested in the integer part 1 .
It is the first character of the hexadecimal number. In this case, because of the division by 256, the digit 1 is in the “256th place”.

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Find the balance. That is the remainder of the value to be converted in decimal. Similar to putting division on paper with large numbers, here we will:

Multiply the integer part obtained above by the divisor. In the example problem: 1 x 256 = 256 (or in other words, the digit 1 in the hexadecimal number represents 256 in base 10).
Subtract the product from the number being divided. 495 – 256 = 239 .

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Divide the difference by the next highest power of 16. Compare with the list of powers above. Move down to the next highest power of 16. Divide the difference by this number to find the next character of the hexadecimal number (If the number being divided is less than the divisor, the next character will be 0).

239 ÷ 16 = 14 . Again, we are only interested in the integer part of the quotient.
This is the second character of the hexadecimal number, located at “position 16”. Every number from 0 to 15 can be represented by a hexadecimal character. We will express it in standard notation at the end of this method.

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Continue to find the balance. Similar to the previous step, here we take the trader’s integer part by the divisor and then subtract the product from the divisor. This is the balance that needs to be converted further.

14 x 16 = 224.
239 – 224 = 15, so the remainder here is 15 .

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Repeat until the balance is less than 16. When the resulting balance is between 0 and 15, you can represent it with a single hexadecimal character. That is the last letter of your answer.

The last “character” in our hexadecimal number is 15, which is in “position 1”.

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Express the answer in hexadecimal notation. At this point, we know all the characters of the hexadecimal number. But so far, we’ve only written them in base 10. To represent each character in hexadecimal notation, we need to convert like this:

The digits 0 to 9 are left unchanged.
10 = A; 11 = B; 12 = C; 13 = D; 14 = E; 15 = F
In the example problem, we get the characters (1)(14)(15). With standard notation, our hexadecimal number would be 1EF .

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Review. Once you understand the nature of hexadecimal numbers, checking the answer will be very simple. Convert each character to decimal, multiplying it by the power of 16 corresponding to its place. In the example problem:

1EF → (1)(14)(15)
From right to left, 15 is at 16 ⁰ = 1. 15 x 1 = 15.
The next character is at position 16 ¹ = 16. 14 x 16 = 224.
The next character is at position 16 ² = 256. 1 x 256 = 256.
Adding up, we get 256 + 224 + 15 = 495, which is the given decimal number.

Fast method (residual method)

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Divide decimals by 16. Treat it as integer division, or in other words, stop at the integer part instead of continuing.

Take for example the number 317,547. 317,547 ÷ 16 = 19,846 , omitting the decimal place after the comma.

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Write the remainder in hexadecimal notation. After dividing by 16, the remainder is the portion that cannot be placed in 16th or higher. Therefore, this balance must be in position 1, the last character of the hexadecimal number.

To find the remainder, multiply the integer part of the quotient by the divisor and then subtract the product from the divisor. Example: 317,547 – (19,846 x 16) = 11.
Convert the character you just found to hexadecimal notation, using the small number conversion table at the top of this page. In the example problem, 11 is converted to B .

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Repeat with the quotient found above. You have converted the balance to hexadecimal characters. Now it’s time to move on with the quotient: divide the quotient by 16. The remainder in this calculation will be the penultimate character of the hexadecimal number. Here, the principle is the same as before: because of the division by (16 x 16 =) 256, the remainder cannot be in the 256 position or greater. Position 1 already exists, so this balance should be in position 16.

In the example problem: 19,846 / 16 = 1240.
Balance = 19,846 – (1240 x 16) = 6 . This is the penultimate character of our hexadecimal number.

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Repeat until the quotient is less than 16. Remember to convert the remainder from 10 to 15 to hexadecimal notation. Write down each balance during the conversion. The last quotient (less than 16) is the first character. With the example problem:

Take the nearest quotient and divide it by 16. 1240 / 16 = 77 remainder 8 .
77 / 16 = 4 remainder 13 = D .
4 < 16, so 4 is the first character.

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Complete hexadecimal numbers. As mentioned, we are looking for each character of the hexadecimal number in order from right to left. Double-check to make sure you’re writing in the correct order.

The final answer is 4D86B .
To check your answer, convert the characters to decimal, multiply by the corresponding power of 16 and add them. (4 x 16 ⁴ ) + (13 x 16 ³ ) + (8 x 16 ² ) + (6 x 16) + (11 x 1) = 317547, given decimal.

Advice

To avoid confusion in using different coefficients, you can include the base below. For example, 512 ₁₀ means “512 in base 10”, a normal decimal number. 512 ₁₆ means “512 in base 16”, which is equivalent to the decimal number 1298 ₁₀ .

Small number conversion

Steps

Intuitive method

Fast method (residual method)

Advice

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