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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.
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 |
Steps
Intuitive method
- If you are completely new to the hexadecimal system, you should learn the basics.
- 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.
- For example, with 495 , we will choose 256 from the list above.
- 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”.
- 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 .
- 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.
- 14 x 16 = 224.
- 239 – 224 = 15, so the remainder here is 15 .
- The last “character” in our hexadecimal number is 15, which is in “position 1”.
- 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 .
- 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)
- Take for example the number 317,547. 317,547 ÷ 16 = 19,846 , omitting the decimal place after the comma.
- 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 .
- In the example problem: 19,846 / 16 = 1240.
- Balance = 19,846 – (1240 x 16) = 6 . This is the penultimate character of our hexadecimal number.
- 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.
- 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 .
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 79,153 times.
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.
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