Decimal to Binary Converter

Binary is base two: every position is a power of two (1, 2, 4, 8, 16...) and a 1 in that position means the power is included. It is the machine's native tongue — flags, bitmasks, subnet math and every permission bit you have ever set all reduce to these place values. Converting decimal to binary by hand means dividing by two and collecting remainders; the converter above just does it.

The From base is pre-set to 10, so type a decimal value and the BIN row shows every bit. The result is exact no matter the size — 9007199254740993 converts to its true 54-bit form, not the rounded float you'd get elsewhere. Negatives carry their sign (sign-magnitude, never two's complement).

FAQ

How do I read a binary number?

Right to left, each position doubles: 1, 2, 4, 8, 16, 32... Add up the positions that hold a 1. 1101 is 8 + 4 + 1 = 13.

Why is my huge decimal value exact here but wrong on other converters?

Most converters parse into a 64-bit float, which loses integers past 2^53. This one accumulates with big integers digit by digit, so nothing is ever rounded.

Does it handle negative numbers?

Yes — sign-magnitude style. -10 becomes -1010: the magnitude converts and the minus sign carries over. Two's complement is not applied because it depends on a bit width.