Converting a base-10 (decimal) number to hexadecimal involves repeatedly dividing the decimal number by 16 and recording the remainders. These remainders, read in reverse order, form the hexadecimal representation.
Here's a detailed explanation of the process:
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Divide by 16: Divide the decimal number by 16. Note the quotient (the result of the division) and the remainder.
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Record the Remainder: The remainder will be a number between 0 and 15. If the remainder is 0-9, it's represented as is. If the remainder is 10-15, it's represented by the letters A-F, respectively (A=10, B=11, C=12, D=13, E=14, F=15).
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Repeat with the Quotient: Take the quotient from the previous division and divide it by 16 again. Record the new remainder.
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Continue Until Zero: Keep repeating this process, dividing the quotient by 16 and recording the remainder, until the quotient becomes 0.
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Read Remainders in Reverse: The hexadecimal representation is formed by reading the remainders from bottom to top (i.e., from the last remainder calculated to the first).
Example:
Let's convert the decimal number 495 to hexadecimal.
| Division | Quotient | Remainder | Hex Value |
|---|---|---|---|
| 495 / 16 | 30 | 15 | F |
| 30 / 16 | 1 | 14 | E |
| 1 / 16 | 0 | 1 | 1 |
Reading the remainders from bottom to top, we get 1EF. Therefore, 495 in decimal is 1EF in hexadecimal.
Summary:
The conversion process is based on finding the largest powers of 16 that fit into the decimal number and their corresponding coefficients. Each hexadecimal digit represents a power of 16, starting from 160 on the rightmost digit and increasing leftward.
