Decimal to Binary Converter

Convert decimal (base 10) numbers to binary (base 2).

Decimal (one number per line)

Binary

Decimal to binary, explained

Binary is the base-2 number system computers use internally: every value is expressed with just the digits 0 and 1. To convert a decimal number, repeatedly divide by 2 and read the remainders bottom-up — e.g. 42 becomes 101010. This tool handles arbitrarily large integers and converts every line locally in your browser — nothing is uploaded.

Built and maintained by Meet Shah · Last updated 19 July 2026

What this tool is used for

Building a bitmask from a decimal value and checking which bits it sets.
Producing a binary constant for a register write or a configuration field.
Checking whether a number is a power of two from its bit pattern.
Working out how many bits a value needs before choosing a field width.
Producing a bit pattern for a teaching example or a datasheet.

Frequently Asked Questions

How do I convert by hand?: Divide by 2 repeatedly and read the remainders bottom-up, or subtract the largest fitting power of two in turn. For 13: 8 + 4 + 1, giving 1101. The second method is faster once you know the powers.
How are fractions represented?: By negative powers of two: 0.5 is 0.1, 0.25 is 0.01. This is why 0.1 decimal is a REPEATING binary fraction and cannot be stored exactly — the root cause of 0.1 + 0.2 === 0.30000000000000004 in almost every language.
How many bits does a number need?: floor(log2(n)) + 1. Values up to 255 need 8 bits, up to 65535 need 16, up to ~2.1 billion need 32 signed. Exceeding the width wraps silently in most languages rather than raising an error.
How are negative values encoded?: Two's complement: invert the bits and add one. The leading bit carries a negative weight, which is why an 8-bit signed range is −128 to 127 rather than symmetric — there is one more negative value than positive.
Why are powers of two everywhere in computing?: Because each additional bit doubles the addressable range. Memory sizes, buffer lengths and array capacities land on 256, 1024, 4096 for that reason, not by convention — it is what binary addressing produces naturally.
How is a fraction converted by hand?: By repeatedly multiplying by two and taking the integer part as the next bit. The process terminates only when the fraction is a sum of powers of two, which is why 0.1 never terminates in binary.
What does a bit shift do to the value?: Each left shift doubles it and each right shift halves it, discarding the shifted-out bit. That is why shifts are used in place of multiplication by powers of two, and why an unintended shift changes a value by orders of magnitude.

Common errors and gotchas

Not padding to the field width, so bit positions shift when the value is placed in a register.
Converting a negative number without fixing the width, which two's complement requires.
Converting a fractional part and expecting termination, which most decimal fractions do not have.
Assuming the output is byte-aligned, when it is only as long as the value needs.
Producing more bits than the target field holds and having the top ones silently dropped.