Number System Converter
Binary, Octal, Decimal & Hexadecimal — all at once
Type a number in any base and see it instantly in all four number systems — no separate tool for each conversion, no copy-pasting between tabs.
Convert a number now — free
Just type the digits — no need for prefixes like 0b, 0x or 0o. Only whole numbers are supported (no decimals or negatives).
Binary, Octal, Decimal & Hex — Reference Table
The first 16 values in every base — worth memorising for quick mental conversions.
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
Need a bigger number? Type it into the calculator above for an instant answer.
Worked Examples
The three methods that cover almost every number system question you'll see in exams.
Convert 44 to binary using repeated division by 2.
- 44 ÷ 2 = 22, remainder 0
- 22 ÷ 2 = 11, remainder 0
- 11 ÷ 2 = 5, remainder 1
- 5 ÷ 2 = 2, remainder 1
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
- Read the remainders bottom to top
Convert 101100 to decimal using positional values.
- Assign powers of 2 from the right: 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
- 1·32 + 0·16 + 1·8 + 1·4 + 0·2 + 0·1
- 32 + 0 + 8 + 4 + 0 + 0
Convert 255 to hexadecimal using repeated division by 16.
- 255 ÷ 16 = 15, remainder 15 (F)
- 15 ÷ 16 = 0, remainder 15 (F)
- Read the remainders bottom to top
Convert 2F to binary using the 4-bit nibble shortcut.
- Convert each hex digit separately to 4 binary bits
- 2 → 0010
- F → 1111
- Join the groups: 0010 1111
Try any of these with the shortcut chips in the calculator above, or swap in your own numbers.
Free Number System Converter — Binary, Octal, Decimal & Hex
Computers represent everything — numbers, text, colours, instructions — using binary (base 2), but binary gets long and hard to read quickly, which is why octal (base 8) and especially hexadecimal (base 16) are used as shorthand. This number system converter takes a single number in any of these four bases and shows you its value in all the others at once, instead of making you pick one conversion direction at a time.
This topic is a standard part of Class 11–12 Computer Science and first-year engineering syllabi, covering conversions like decimal to binary, binary to decimal, decimal to hex and hex to binary. The three methods worth actually learning — not just memorising — are: repeated division by the target base (for converting out of decimal), multiplying by positional place values (for converting into decimal), and the 4-bit nibble shortcut for jumping directly between hexadecimal and binary without going through decimal at all.
Hexadecimal is especially common in real systems because each hex digit maps to exactly 4 binary bits, so a byte (8 bits) is always exactly 2 hex digits — that's why you'll see colours written as 6-digit hex codes, and memory addresses or MAC addresses written in hex rather than long binary strings.
Every conversion here uses exact integer arithmetic (not floating-point), so even long binary strings convert correctly without rounding errors. Need something else? Try the data storage converter for bits, bytes, KB and MB, or head back to the unit converter hub for everything else.
← Back to all unit convertersNumber systems — common questions
Multiply each binary digit by its positional power of 2 (starting from 2⁰ on the right) and add the results. For example, 101100 = 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 0×1 = 44.
Divide the number by 2 repeatedly, writing down the remainder each time, until you reach 0. Then read the remainders from bottom to top. For example, 44 converts to 101100.
Convert each hexadecimal digit on its own into exactly 4 binary bits, then join the groups together. For example, 2F becomes 0010 (for 2) followed by 1111 (for F), giving 00101111.
Multiply each octal digit by its positional power of 8 and add the results. For example, 254 (octal) = 2×64 + 5×8 + 4×1 = 172 in decimal.
Because each hex digit represents exactly 4 binary bits, hexadecimal gives a short, human-readable way to write long binary values — a full byte is always exactly 2 hex digits. This is why colour codes, memory addresses and MAC addresses are usually written in hex.
Yes. Number systems and base conversion are a standard topic in Class 11-12 Computer Science and first-year engineering courses, and this converter covers the same binary, octal, decimal and hexadecimal conversions tested in those exams.