Binary Converter
Type in any base — all four representations update live.
What Is a Binary Converter?
Computers think in binary — base 2, just 0s and 1s — while programmers and engineers navigate between four number systems constantly: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). This converter keeps all four fields in sync: type a value in any one of them and the other three update instantly. It is the quick reference you need for computer science homework, embedded programming, color codes, memory addresses, and network masks.
The four bases coexist because each is best at something. Binary shows the machine's actual state — every bit a wire on or off. Hexadecimal compresses binary into readable shorthand (each hex digit is exactly four bits, so FF = 11111111). Octal survives mainly in Unix file permissions. Decimal is where humans live. Fluency means translating without thinking; until then, there is this page.
How to Use the Binary Converter
- Type your value into any field — Decimal, Hexadecimal, Binary, or Octal.
- The other three fields convert automatically as you type.
- Copy whichever representation you need; to start over, clear the field and type a new value.
How Base Conversion Works
Each system counts in powers of its base. In binary, digit places are worth 1, 2, 4, 8, 16... so 1011 means 8 + 0 + 2 + 1 = 11 in decimal. Hexadecimal extends digits past 9 with letters A–F (A = 10, F = 15), and its places are worth 1, 16, 256... The binary–hex shortcut professionals use: group binary digits in fours from the right and convert each group — 1111 1111 becomes F F. Octal works the same way in groups of three. Place-value expansion in the other direction — repeatedly dividing by the target base and reading remainders upward — converts any decimal value by hand.
Where You'll Meet These Numbers
- Hex colors: #FF5733 is three hex bytes (red 255, green 87, blue 51) — this converter confirms what each byte means in decimal.
- Permissions and masks: Unix chmod 755 is octal; subnet masks like 255.255.255.0 become long binary strings network engineers read fluently.
- Low-level programming: bit flags, register values, and memory dumps are documented in hex because binary is too long and decimal hides the bit patterns.
Why does hexadecimal use the letters A through F?
Base 16 needs sixteen distinct digit symbols, but ordinary numerals stop at 9. The convention — settled in the early computing era — borrows A, B, C, D, E, F to stand for 10 through 15. Case does not matter: FF, ff, and Ff are all 255 in decimal and 11111111 in binary.
How large a number can this converter handle?
It comfortably handles everyday values — colors, character codes, typical addresses and counts. Extremely long binary strings (dozens of digits) can exceed the precise integer range of JavaScript arithmetic (about 9 quadrillion, or 2^53), beyond which results may lose exactness in the last digits. For typical learning and engineering use, you will not approach that limit.
What is the difference between binary and ASCII?
Binary is a number system; ASCII is a code that assigns numbers to characters — A is 65, a is 97, 0 (the digit) is 48. Converting text to binary is really two steps: character → its code number (in decimal), then that number → binary. The Text to Binary tool on this site performs the full two-step conversion for whole strings.
How do I convert decimal to binary by hand?
Repeatedly divide by 2, recording each remainder (0 or 1), until the quotient is 0 — then read the remainders from last to first. For 13: 13÷2 = 6 r1, 6÷2 = 3 r0, 3÷2 = 1 r1, 1÷2 = 0 r1 → reading upward gives 1101. Verify here: 1101 binary should show 13 in the decimal field.