Base Converter guide
Why Do Computers Use Binary?
Computers use binary because electronic components are far more reliable with two states than with more. A circuit only needs to tell "on" from "off", which tolerates noise and voltage drift, whereas distinguishing ten voltage levels would demand precision that is expensive and fragile.
It is about reliability, not maths
There is nothing mathematically special about base 2. You could build a computer in base 10, and some early machines genuinely tried.
The reason binary won is engineering. A transistor is essentially a switch, and asking a switch whether it is on or off is a question it can answer reliably billions of times a second.
Asking it to report one of ten distinct voltage levels is a much harder question, and the answer gets less trustworthy as components age, warm up, or sit near something noisy.
The noise margin
This is the heart of it. Suppose a circuit runs at 5 volts. In binary, anything below about 1.5V counts as 0 and anything above about 3.5V counts as 1. There is a two-volt gap in the middle where nothing is decided.
That gap is enormous. Voltage can sag, spike or pick up interference and the answer still comes out right.
Now split the same 5 volts into ten levels. Each one gets about half a volt, with a fraction of that as margin. Small amounts of interference start turning 6s into 7s, and there is no way to tell that it happened.
Binary is not the most compact way to store information. It is the most robust, and robustness is what matters when you are doing billions of operations a second.
Everything else follows from it
Once you commit to two states, a lot of things fall into place neatly.
Boolean logic — AND, OR, NOT — maps directly onto circuits, so arithmetic can be built out of a handful of simple gate types.
True and false, yes and no, on and off all map onto the same 1 and 0, so logic and arithmetic share one representation.
And error detection becomes tractable. Since only two values are possible, a corrupted bit can often be detected and sometimes corrected, which is much harder with ten states.
The machines that tried other bases
Base 10 was genuinely attempted. ENIAC, in 1945, stored decimal digits directly using rings of ten vacuum tubes. It worked, but it needed ten tubes to store what one bit stores now, and any tube failing corrupted the digit.
Base 3 is arguably more elegant. The Soviet Setun computer, built in 1958, used balanced ternary with states of −1, 0 and +1. It handled negative numbers beautifully and needed fewer digits per number.
It was never adopted, because reliable three-state components were harder to manufacture than two-state ones, and by then the industry had standardised. Binary was not chosen because it was best in theory — it was chosen because it was easiest to build well, and everything since has been built on top of that decision.
Where this shows up for you
The binary foundation leaks into things you notice.
File sizes come in powers of two — 1024 rather than 1000 — because memory is addressed in binary.
The decimal 0.1 cannot be stored exactly in binary, in the same way 1/3 cannot be written exactly in decimal. That is why 0.1 + 0.2 comes out as 0.30000000000000004 in most programming languages.
And integer limits land on odd-looking numbers: 255, 65535, 2147483647. Each is one less than a power of two, and each has been the cause of a memorable bug somewhere.
