This calculator writes a nonnegative base-10 integer in hexadecimal, or base 16. The value does not change; only its notation changes. Hexadecimal uses the digits 0 through 9 and the letters A through F, where A represents 10 and F represents 15.
Hex is common in computing because one hexadecimal digit corresponds neatly to four binary bits. You may see it in color values, memory addresses, byte displays and debugging output.
The browser field uses whole-number steps, and the server verifies that the input is a nonnegative integer. No prefix such as 0x is added. Therefore decimal 255 is displayed as FF rather than 0xFF.
A hexadecimal numeral with digits dₙ…d₁d₀ has decimal value:
value = Σ(dᵢ × 16ⁱ)
To convert a decimal integer by hand, divide repeatedly by 16 and record each remainder. Replace remainders 10–15 with A–F, then read the remainders from last to first. Zero is written as 0.
Hex digits have values 0, 1, …, 9, A=10, B=11, C=12, D=13, E=14 and F=15. Place values from right to left are 1, 16, 256, 4096 and so on.
| Term | Meaning | Example |
|---|---|---|
| Decimal input | A nonnegative base-10 integer | 254 |
| Base | The number of digit values in the target system | 16 |
| Remainder | A value from 0 to 15 produced during repeated division | 14 becomes E |
| Hex output | The same integer written with 0–9 and A–F | FE |
Convert decimal 254. Divide by 16:
254 ÷ 16 = 15 remainder 14. Remainder 14 is E. Then 15 ÷ 16 = 0 remainder 15, and remainder 15 is F. Read the remainders upward to get FE.
Check with place values: F×16 + E×1 = 15×16 + 14 = 240 + 14 = 254. Another useful boundary is decimal 16, which becomes 10 in hexadecimal: one group of sixteen and zero ones. Decimal 255 is FF, while 256 is 100.
The output is a numeral, not a different quantity. FE in this result means base 16; without context, the text “10” could mean decimal ten or hexadecimal sixteen. Add a label or conventional 0x prefix when sharing the value in technical work.
Leading zeros do not change an integer’s value, so 00FF and FF both represent 255. They can still matter in a fixed-width field: a byte is often displayed as two hexadecimal digits. This page removes such formatting and returns the shortest numeral.
Do not treat the letters as variables or ordinary text. Each is one digit with a defined numeric value.
You can verify a hexadecimal result through binary. Replace each hex digit with four bits: 0 through F correspond to 0000 through 1111. For example, 2A becomes 0010 1010. Reading that binary value as decimal gives 32+8+2=42. This method is especially convenient for byte values, where two hex digits cover eight bits.
The mathematical conversion has no chosen byte width. Software storage does. Decimal 300 converts correctly to hex 12C, but it cannot fit in one unsigned byte because one byte stops at FF, or 255. Decide the required storage width separately and add leading zeros only after conversion. For example, a 16-bit display might write 42 as 002A. The calculator’s shorter 2A has the same numeric value.
When checking a long result, expand one place at a time and add the products. This is slower than software conversion but catches transposed digits and base confusion. Keep the original decimal value beside the converted form when accuracy matters.
They are single digits for values 10 through 15. This lets base 16 represent sixteen possible digit values without using two-character decimal numbers.
The rightmost hex place holds ones and the next holds sixteens. One sixteen plus zero ones is written 10 in base 16.
This page accepts nonnegative integers only. Signed computer representations depend on a chosen bit width and encoding, so a negative conversion would need more information.
No. Hexadecimal digits are case-insensitive in ordinary use. The calculator displays uppercase letters for consistency.
Each hex digit represents exactly four binary bits. F corresponds to 1111, so hex FF corresponds to binary 11111111.
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