Binary Converter

Binary is the native language of every computer, and sooner or later anyone who studies computing, configures permissions or debugs low-level code has to read it by eye. This converter translates binary numbers into the decimal, hexadecimal and octal values people think in — and works the other way too — so a string of ones and zeros stops being a wall and becomes a number you can reason about.

Quick Answer

To read a binary number, add up the place values where a 1 appears: each position is worth a power of two, doubling from 1 at the right (2⁰, 2¹, 2², 2³…). For example, 11010110₂ = 214, because 128 + 64 + 16 + 4 + 2 = 214. Grouping the same bits three at a time gives octal (326₈) and four at a time gives hexadecimal (D6).

Place Value in Base Two

Decimal feels natural only because it has ten symbols and your hands agree with it. Binary runs the identical system with two symbols, 0 and 1, called bits. The rightmost bit counts units, the next counts twos, then fours, eights, sixteens — the place values are powers of two instead of powers of ten. A byte, eight bits, therefore spans 0 to 255, a range that turns up everywhere from colour channels to network addresses because hardware was built around it.

Reading binary is addition with most of the terms missing. Write the place values over the digits and keep only the ones under a 1. It helps to memorise the first eight powers — 1, 2, 4, 8, 16, 32, 64, 128 — since every byte you'll ever meet is a sum of those. Writing a decimal number in binary runs in reverse: find the largest power of two that fits, subtract it, mark a 1 in that position, and continue with what remains until nothing is left.

Octal and hexadecimal exist as shorthand for binary, not as separate worlds. Three bits max out at 7, exactly one octal digit, so binary groups cleanly into octal from the right. Four bits max out at 15, one hexadecimal digit (0–9 then A–F), so binary also groups cleanly into hex. This is why programmers think in hex: it is binary with the monotony compressed out, four bits per digit with no arithmetic lost.

How to Use the Binary Converter

1. Enter the binary number you want to translate — digits 0 and 1 only; spaces used to group bits in your notes should be left out or kept only where the tool accepts them.
2. Read the decimal equivalent first if you need the human-scale value of the number.
3. Check the hexadecimal and octal forms when your goal is compact notation — file permissions, colour codes, memory dumps or configuration values.
4. To convert the other way, enter a decimal number and read its binary form, noting the bit pattern rather than just the digits.
5. Verify a hand calculation by converting the result back; a correct round trip returns your starting number exactly.
6. For whole files of text rather than numbers — turning letters into their binary codes — use the dedicated text tool linked below instead.

Worked Example: Decoding 11010110

Take the byte 11010110. Lay the place values over it: 128, 64, 32, 16, 8, 4, 2, 1. The 1s sit under 128, 64, 16, 4 and 2. Add them: 128 + 64 = 192; 192 + 16 = 208; 208 + 4 = 212; 212 + 2 = 214. Now the shorthand forms. Group from the right in threes — 011 010 110 — giving octal digits 3, 2, 6, so 326₈, and check: 3×64 + 2×8 + 6 = 214. Group in fours — 1101 0110 — giving hex digits D (13) and 6, so D6, and check: 13×16 + 6 = 214. Three notations, one number, each derivable from the bits in seconds once grouping becomes habit.

Binary Blunders Worth Avoiding

The most common mistake is reading a binary string as if it were decimal — treating 1010 as "one thousand and ten" rather than ten. The second is grouping from the left when forming octal or hex; groups must be counted from the right, padding the leftmost group with leading zeros, or every digit after the first lands wrong. Third, dropping leading zeros matters in fixed-width contexts: the byte 00001111 and the number 1111 are the same value but not the same pattern, and in permissions, flags and masks the pattern is the point.

Finally, know where plain conversion stops. Negative numbers in real systems are stored in two's complement form, fractions in floating point, and both follow extra rules beyond place value; a raw converter shows you the unsigned pattern, and interpreting a signed or floating-point pattern is a separate step. Signed 8-bit values, for instance, treat the leftmost bit as a sign indicator, so 11111111 represents −1 rather than 255 in that context. Keep the width in view when comparing patterns, too, because the same value looks entirely different written at 8, 16 or 32 bits, and only the width tells you which pattern a system actually stored.

Two encounters with binary reward fluency more than most. The first is file and memory sizes: a byte is 8 bits, and the kilobyte of everyday speech is 1,024 bytes — 8,192 bits — which is why storage figures come in powers of two wearing decimal-looking costumes. The second is network addresses. An IPv4 address such as 192.168.0.1 is four bytes in disguise, each number an octet between 0 and 255; the first octet, 192, is the byte 11000000. Reading a subnet mask like 255.255.255.0 in binary — twenty-four 1s followed by eight 0s — is what makes the notation /24 stop being jargon and become a picture of exactly where the network part of the address ends.

Keep Exploring Number Systems

Decimal is usually the other end of the journey: the Decimal Converter turns ordinary base-ten numbers into binary, hexadecimal and octal in one pass, and the Hex Converter focuses on the base-sixteen notation that colour codes and memory addresses use. All of the site's conversions live together in the converters section.