💻 Number Base Converter
Computers work internally in binary, and programmers often use hexadecimal notation for memory addresses and colour codes. Enter an ordinary decimal number to see it instantly converted to binary, octal and hexadecimal — handy for programming, networking or number-system homework.
Formula
Each base expresses the same number using a different number of symbols: value = Σ (digit × base^position)
Decimal (base 10) uses digits 0-9. Binary (base 2) uses only 0 and 1: each position represents a power of 2. Octal (base 8) uses 0-7, with powers of 8. Hexadecimal (base 16) uses 0-9 and A-F (where A=10 through F=15), with powers of 16. The number itself never changes — only the way it is written down.
Steps
- 1Enter a decimal (base 10) whole number, from 0 to 4,294,967,295.
- 2The calculator instantly converts it to binary, octal and hexadecimal.
- 3Read off the three results, plus the decimal number for reference.
Decimal, binary, octal and hexadecimal compared
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 8 | 1000 | 10 | 8 |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 128 | 10000000 | 200 | 80 |
| 255 | 11111111 | 377 | FF |
Each step in the decimal column doubles the value and adds a digit in the other bases.
commonMistakes
- Reading hexadecimal letters (A-F) as separate characters rather than as the values 10 through 15.
- Assuming the leftmost digit is always the "units"; in every base it is actually the rightmost digit that is the unit (position 0).
- Forgetting that a negative number or a decimal fraction cannot go directly into this field; it only works for whole numbers from 0 upward.
useCases
- Understanding and building colour codes such as #FF5733 in web design.
- Debugging memory sizes, IP addresses and error codes shown in hex or binary.
- Checking homework or exams about number systems without converting by hand.