Binary to decimal converter
1011 in binary is 11 in decimal: 1×8 + 0×4 + 1×2 + 1×1. Going the other way is repeated division — 11 ÷ 2 eight times, reading the remainders upwards — and both sums are printed rather than only their answers, because the sum is what the question is usually about.
Convert between binary, octal, decimal and hex in any direction — and see how. Converting into decimal prints the place-value sum; converting out of it prints the repeated division, which is the method taught on paper and the one the question is usually about.
Conversions checked against arbitrary-precision arithmetic in the test suite · How we check
- Binary
- 1011
- Octal
- 13
- Decimal
- 11
- Hex
- b
Place values — binary to decimal
| Digit | Place | Contributes |
|---|---|---|
| 1 | 23 = 8 | 8 |
| 0 | 22 = 4 | 0 |
| 1 | 21 = 2 | 2 |
| 1 | 20 = 1 | 1 |
| Sum | 11 | |
Nought to sixteen, in four bases
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 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 |
| 16 | 10000 | 20 | 10 |
Sixteen is where hex rolls over to 10 and binary to 10000 — the same event in both, one digit later in one than in the other.
The powers of two worth knowing
| Power | Decimal | Hex | Where it shows up |
|---|---|---|---|
| 24 | 16 | 10 | one hex digit |
| 25 | 32 | 20 | a 32-character alphabet |
| 26 | 64 | 40 | a six-bit field |
| 27 | 128 | 80 | the ASCII range, 0 to 127 |
| 28 | 256 | 100 | one byte — 0 to 255 |
| 210 | 1024 | 400 | a kibibyte, 1024 bytes |
| 216 | 65536 | 10000 | the range of a 16-bit port number |
| 220 | 1048576 | 100000 | a mebibyte |
Questions people actually ask
- How do you convert binary to decimal?
- Give each digit the weight of its column and add. Columns are powers of two from the right: 1, 2, 4, 8, 16 and so on. 1011 is 8 + 0 + 2 + 1 = 11. The table above prints one row per digit so the sum can be checked by hand.
- How do you convert decimal to binary?
- Divide by two repeatedly and keep the remainders, then read them bottom to top. 11 ÷ 2 is 5 remainder 1, 5 ÷ 2 is 2 remainder 1, 2 ÷ 2 is 1 remainder 0, 1 ÷ 2 is 0 remainder 1 — bottom to top, that is 1011.
- Why is hex easier to read than binary?
- Because four binary digits are exactly one hex digit, with no arithmetic in between. 1111 is F, 1010 is A, and any byte is two hex characters. Splitting the binary into groups of four from the right and looking each group up is the whole conversion — which is why memory dumps and colour codes are written in hex rather than in binary.
- What is 11111111 in decimal?
- 255. Eight ones is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, and that is why a byte holds 0 to 255 and why FF is the largest two-digit hex value. It is also why colour channels stop at 255.
- What is the largest number here?
- There is no ceiling. The arithmetic runs on arbitrary-precision integers, so a 200-digit binary number converts exactly. An ordinary calculator loses digits past 9,007,199,254,740,991 — 2⁵³ — because it stores numbers as floating point.
- Does this handle negative numbers?
- It converts them with a minus sign, which is how people write them on paper. It does not show two's complement, because that depends on a word width — −5 is 11111011 in eight bits and 1111111111111011 in sixteen — and the number alone does not say which.
Cite this page
- APA
- Rule Calculator. (2026). Binary to Decimal Converter. Rule Calculator. https://rulecalculators.com/binary-to-decimal
- MLA
- "Binary to Decimal Converter." Rule Calculator, August 16, 2026, https://rulecalculators.com/binary-to-decimal.
- Chicago
- Rule Calculator. "Binary to Decimal Converter." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/binary-to-decimal.
The date is when the figures on this page were last checked against their source, not the day you opened it. Add your own access date if your style needs one.