bit

A bit is one binary decision. Eight of them make a byte, which is enough to distinguish 256 things, which is why a byte held one character for most of computing history.

The useful thing to carry is that bits count doublings. Each bit added doubles the number of distinct values: 8 bits gives 256, 16 gives 65,536, 32 gives about 4.3 billion. That is why key sizes are quoted in bits — a 128-bit key is not twice a 64-bit key, it is 2⁶⁴ times as many keys, which is about 18 quintillion times.

That doubling is also why bits of security strength can never be a unit conversion on this site. Going from bits to a number of keys is 2ⁿ, an exponential, and the conversion engine here multiplies and adds — it cannot raise to a power. So the relationship lives in a formula, in the same way a decibel does. A unit that pretended to convert 128 bits into 3.4 × 10³⁸ keys would be lying about what kind of relationship it is.

Shannon's other contribution matters for anyone computing password strength: the bits in an entropy figure describe how a value was chosen, not what it looks like. Eight random bits are eight bits of entropy. Eight bits that always spell the same letter are none.