Why Computers Use Binary, Not Decimal
"Everything is just 1s and 0s" gets repeated in textbooks, videos, and offhand explanations constantly, as if that settles the question, without ever actually explaining why binary specifically, rather than the ten digits everyone already counts with. Ten fingers made decimal the obvious choice for human arithmetic. Computers ended up on two digits instead, for reasons that have nothing to do with counting and everything to do with electrical reliability.
Binary arithmetic predates electronic computers by two centuries
Gottfried Leibniz published a full description of binary arithmetic in 1703, in an essay partly inspired by his study of the hexagrams of the I Ching. A genuinely documented historical connection, though how much direct influence it actually had is still debated by historians. Either way, the mathematics of binary counting was fully worked out long before any machine existed that needed it.
Early computers actually tried decimal first
Binary wasn't the obvious engineering choice from day one. ENIAC, one of the first electronic general-purpose computers (1945), used decimal representation internally. Binary won out over the following years for a specific, practical reason: electronic circuits are far more reliable distinguishing between just two states. Voltage present or absent, "on" or "off". Than reliably distinguishing among ten different voltage levels for decimal digits, where small electrical noise could flip a reading between adjacent values.
That's the part usually missing from "it's all 1s and 0s": the reason isn't philosophical or arbitrary, it's a specific, measurable engineering tradeoff. Telling two voltage states apart reliably is easy; telling ten apart reliably, with noise in the circuit, is not. Once that's clear, the phrase stops being a slogan to just accept and turns into something you could actually explain to someone else.
The theoretical case was made by a landmark thesis
Claude Shannon's 1937 master's thesis showed that Boolean algebra. True/false logic. Could be directly implemented using electrical switching circuits, giving engineers a rigorous mathematical foundation for building logic (and therefore computation) out of simple on/off switches. It's frequently cited as one of the most consequential master's theses of the 20th century, and it's the theoretical bridge between "binary is mathematically convenient" and "binary is what we should actually build hardware out of."
Why hex shows up as a human-friendly shortcut
Hexadecimal (base 16) isn't a competing system to binary. It's a compact way for humans to read and write it. Each hex digit maps exactly onto 4 binary digits (a "nibble") with nothing left over, because 16 is a power of 2. Decimal doesn't divide evenly into binary groupings at all, which is exactly why programmers use hex as shorthand for binary data but essentially never use decimal for the same purpose.
What to actually do with this
If the goal is being able to explain why computers use binary in your own words, the short, accurate version is: electrical circuits reliably distinguish two states far more easily than ten, and the theoretical groundwork (Shannon's thesis) showed how to build actual logic out of those two states. If the goal is working with binary or hex day to day, hex is the practical shortcut worth learning first, since it maps cleanly onto binary in a way decimal never will. If the goal is just satisfying curiosity about a phrase you've heard a hundred times, the honest answer is that it's a hardware decision, not a mathematical law: decimal computers were built and worked, they just lost out to a more reliable alternative.
Convert between binary, decimal, and hex, or encode text as binary, with the binary/hex converter.