★ PROVEN TRAFFIC TOPIC · MATH · NUMBER BASES
Hexadecimal is base 16, so its digits run 0–9 and then A–F for ten through fifteen — and every byte you have ever seen written as two hex characters is just a decimal number in disguise. At the defaults, 255 in decimal is FF in hexadecimal: 255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15, so reading the remainders from the bottom up gives F followed by F. Flip the direction switch to convert hex back to decimal, with lowercase letters and a 0x prefix both accepted.
Choose the direction, type the value, and the answer appears immediately. Decimal inputs must be whole numbers from 0 to 999,999,999; hex inputs use digits 0–9 and letters A–F, lowercase accepted, with or without a 0x prefix. The converter shows the answer in capitals, because that is how hex is conventionally written.
To convert decimal to hex, divide by 16, write down the remainder, and repeat with the quotient until the quotient is 0. Then read the remainders from the last one to the first — bottom to top. Remainders 10 through 15 become letters A through F. To convert hex to decimal, do the reverse: expand each digit times its power of 16 and add. F in the units place is worth 15, F in the sixteens place is worth 15 × 16 = 240, and so on.
Setup: convert decimal 255 to hexadecimal.
Line 1 — divide. 255 ÷ 16 = 15 remainder 15 (F).
Line 2 — divide again. 15 ÷ 16 = 0 remainder 15 (F). The quotient is 0, so stop.
Line 3 — read bottom to top. The remainders, read last to first, are F then F: FF.
Line 4 — check by expanding. F × 16 + F = 15 × 16 + 15 = 240 + 15 = 255. The conversion checks out.
16 ÷ 16 = 1 remainder 0; 1 ÷ 16 = 0 remainder 1. Read bottom to top: 10. This is the cleanest illustration of the base: 10 in hex means one sixteen and zero ones, exactly as 10 in decimal means one ten and zero ones.
4095 ÷ 16 = 255 remainder 15 (F); 255 ÷ 16 = 15 remainder 15 (F); 15 ÷ 16 = 0 remainder 15 (F). Read bottom to top: FFF. Check: 15 × 256 + 15 × 16 + 15 = 3840 + 240 + 15 = 4095. Three F digits are the largest three-digit hex number, just as 999 is the largest three-digit decimal number.
Zero is zero in every base: decimal 0 converts to hex 0, with no division steps needed. Edge cases like this are where converters most often break, so it is worth stating: the answer is 0, not an empty string and not an error.
Flip the direction and enter FF: F × 16 + F = 240 + 15 = 255. Enter lowercase ff and you get the same 255, because hex letters are case-insensitive. Enter 0xFF and you also get 255, because the 0x prefix is stripped before conversion — it is a label that says “this is hex,” not part of the number.
| Output | Formula | What it means |
|---|---|---|
| Hexadecimal digit | remainder of division by 16; 10–15 → A–F | Each step of the 255 example leaves remainder 15 (F), twice. |
| Full hex value | remainders read last to first | FF for 255 — reading top to bottom instead would still give FF here, but would be wrong in general. |
| Decimal check | Σ digit × 16position | 255 for FF: 15 × 16 + 15. Always expand to verify a conversion. |
Conversions are exact integer arithmetic within the stated range: decimal inputs from 0 to 999,999,999, whose largest hex form is 3B9AC9FF. The converter does not handle fractions, negative numbers, or values above that ceiling, and it does not guess at ambiguous input — a decimal point, a minus sign, a letter outside A–F, or an empty box is reported as an error with a reason, not silently rounded or truncated. Hex input is case-insensitive and an optional 0x prefix is accepted; anything else in the box is rejected. Error policy: negative decimal values, non-integer decimals, non-hex characters, empty input, and values above 999,999,999 are all reported as errors rather than modeled.
Bright Side Kit. "Decimal to Hex Converter: Two-Way Tool." https://brightoolbox.com/decimal-to-hex/ Accessed October 24, 2026.Data sourcesFF. 255 ÷ 16 = 15 remainder 15 (F), and 15 ÷ 16 = 0 remainder 15 (F); reading the remainders bottom to top gives FF. Check: 15 × 16 + 15 = 255.
Divide by 16 repeatedly and read the remainders backwards. Each remainder is one hex digit (10–15 become A–F); stop when the quotient reaches 0, then read the remainders from the last division to the first.
10. 16 ÷ 16 = 1 remainder 0, then 1 ÷ 16 = 0 remainder 1, so the digits read bottom to top are 1 and 0. Hex 10 means one sixteen, just as decimal 10 means one ten.
255. Expand it: F × 16 + F = 15 × 16 + 15 = 240 + 15 = 255. Lowercase ff and the prefixed form 0xFF convert to the same 255.
No. Uppercase FF and lowercase ff are the same number, and this converter accepts both, with or without a 0x prefix. The converter displays capitals by convention, but it reads either case.
Because one hex digit is exactly four bits. A byte (eight bits) is exactly two hex digits, so values like FF (255) or 0xFF map cleanly onto memory, colors, and register values without the long strings of binary.
999,999,999 in decimal, which is 3B9AC9FF in hex. Anything larger is reported as an error rather than truncated, so a too-large input can never silently give a wrong answer.