Binary

Binary is the base-2 number system, representing all values using only the digits 0 and 1. Each digit is a bit, 8 bits form a byte, and every piece of digital information, from this sentence to a bitcoin private key, is ultimately a sequence of bits.

Why it matters

Binary is the reason digital scarcity had to be invented rather than assumed. Bits copy perfectly and cost nothing to duplicate, which is why digital money defeated computer scientists for decades: any digital coin could simply be copied and spent twice. Bitcoin's breakthrough was making a particular arrangement of bits, a ledger entry, impossible to duplicate without redoing the physical work of the world's miners. Its core quantities are binary through and through: private keys are 256-bit numbers, SHA-256 produces 256-bit hashes, and all balances are integers counted in satoshis.

How it works

Each position in a binary number represents a power of 2, so 1011 means one 8, no 4, one 2, and one 1, or eleven. The security of bitcoin's keys comes from the size of this space: 2 to the power of 256 is a number with 78 digits, so many possible private keys that guessing one by brute force would outlast the energy of stars. Gold's scarcity rests on the rarity of an element in the earth's crust; bitcoin's rests on the arithmetic of large binary numbers, enforced by cryptography rather than geology.