Decimal to Binary Converter — Encode Numbers as Binary Code

Take an ordinary base-10 integer and rewrite it as a string of 0s and 1s. The page runs everything through JavaScript BigInt, so values far above 2⁵³ still convert without rounding errors. Negatives and decimals are rejected on purpose.

How decimal to binary works

Repeatedly divide the decimal number by 2 and write down the remainder. Reading the remainders from the last division back to the first gives the binary digits. For example, 13 → 1101 (13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1).

Quick examples

How to use

1. Type a non-negative whole number (no minus sign, no decimal point) into Input.
2. The binary string appears in Output with no leading zeros. Pad manually if you need a fixed byte width.
3. Need the reverse? Click Binary → Decimal at the top, or use Swap.
4. Hit Copy to grab the result. Processing is entirely local.

Real-world use cases

• Building bitmasks. When firmware code reads or writes individual hardware-register bits — interrupt flags, permission bits, feature toggles — turning the desired decimal mask into binary tells you which positions get a 1.
• Subnet and netmask reasoning. A netmask like 255.255.255.0 is really four bytes, three of which translate to 11111111. Converting the octets to binary makes it obvious that the prefix length is 24, and the same trick exposes off-by-one mistakes in /27 versus /28.
• IoT and embedded encoding. Squeezing a sensor reading into a fixed bit field — say, 10 bits for temperature inside a 32-bit telemetry word — starts by turning the value into binary and checking it fits the budget.
• Teaching the divide-by-2 algorithm. Students who run the converter alongside paper division learn faster than from a textbook table, because the tool confirms each remainder.
• Truth tables and digital logic. Before writing the output column, students enumerate input combinations 0..7 as 000..111; the converter is a quick sanity check.
• CTF and puzzle payloads. Many challenges hide a flag or coordinate inside a long bit string. Encoding the target as binary, then comparing to the puzzle output, is a standard first step — feed the result back through Binary to Decimal to verify the round trip.

How decimal turns into binary — the divide-by-2 method

Every positive integer has exactly one base-2 representation, and the textbook way to find it is the divide-by-2 method: keep dividing by 2, keep the remainders (each is a 0 or 1), and read the remainders bottom to top. With 13 you get 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 — read upwards and the answer is 1101. The remainders are forced to be 0 or 1 because that is what division by 2 produces, which is why the algorithm works for any base by simply changing the divisor.

The idea of writing numbers with only two digits goes back a long way. Gottfried Wilhelm Leibniz laid out a systematic positional binary notation in 1703 in his paper Explication de l'Arithmétique Binaire, complete with addition and multiplication tables. For more than two centuries the notation was a curiosity, until George Stibitz built the Model K relay adder at home in 1937 and Konrad Zuse finished the mechanical, binary-by-design Z1 in 1938. ENIAC, completed in 1945, was famously a decimal machine, but every general-purpose computer that followed it leaned on binary internally — partly because Shannon's 1937 master's thesis had shown that relay circuits realised Boolean algebra cleanly.

All conversion in this tool runs through JavaScript BigInt, so the divide-by-2 chain works on arbitrary-precision integers — a 40-digit decimal converts exactly, with no silent rounding around 2⁵³. If you tick the Signed (two's complement) checkbox and pick a bit width, the encoder also accepts negatives: -128 at 8 bits becomes 10000000, the same bit pattern you'd see in a CPU register or a signed byte field on the wire.

Worked examples

Click each example to expand the step-by-step trace:

Common pitfalls

• Negatives are refused by default. Plain base-2 has no sign, so the tool rejects -5 unless you switch into signed mode by ticking Signed (two's complement) and picking a bit width.
• Signed mode needs a bit width. Once signed is on, the converter has to know whether you mean an 8-, 16-, 32-, or 64-bit field. Values outside the range — -129 at 8 bits, or 200 at 8 bits — are rejected instead of being silently truncated.
• No fractional input. 0.5 and 3.14 are not integers, so the tool refuses them. Real-number conversion is an IEEE-754 problem, not a base-conversion one.
• BigInt removes the 2⁵³ ceiling. Plain JavaScript Number starts to lose precision above 2⁵³, but this converter routes the value through BigInt, so a 30-digit decimal still produces an exact bit string.
• Thousands separators are not parsed. 1,024 with a comma is rejected; type 1024 instead. Stray whitespace at the ends is tolerated, but embedded punctuation is not.

Need to go the other way? The binary to decimal converter reverses every example above, and the binary to hex converter compresses 8-bit groups into two hex digits when the binary form gets unwieldy. For converting plain English to and from binary instead of numeric values, hop over to the binary code translator.