← Binary Course — Part A, lesson 1 of 4 (Counting in other bases)
1. Why Computers Don't Count in Decimal
The concept
A computer has to store and move numbers using some real, physical property of its hardware: a voltage level, a magnetized spot, a switch's position. Whatever that property is, the machine needs to reliably tell its possible states apart, over and over, for years, cheaply, at high speed — and it has to get that reading right essentially every single time, because a single misread digit silently corrupts the answer.
That reliability requirement is the whole reason computers land on binary (two states) rather than decimal (ten states), and it has nothing to do with computers being unable to "understand" numbers bigger than one. It's an engineering trade-off about margin for error.
If a physical property has some usable range (say, a voltage between "low" and "high"), and you only need to distinguish two states within that range, you can draw a big, generous line between "counts as off" and "counts as on" and leave a wide no-man's-land in between that noise, heat, component aging, and manufacturing tolerance would all have to conspire to cross. If you instead need to distinguish ten states in that same range, the gaps between adjacent states shrink to a tenth the size, and a tenth as much disturbance is now enough to misread a 4 as a 5. Binary isn't the only possible choice — it's the choice that buys the largest error margin for the least engineering effort, which matters enormously when you're building a machine out of thousands or millions of these components and need every single one to be right.
Example 1 — the light switch vs. the dimmer
A plain light switch only has to land in one of two positions, and it's built so those two positions are physically far apart and each has a detent that holds it firmly in place. You could grab it in the dark, half break it, let it collect a decade of dust, and you'd still always be able to tell "on" from "off" correctly.
A dimmer with ten marked positions asks the same physical mechanism (a rotating knob) to land precisely in one of ten narrow zones instead of two wide ones. The same amount of wobble, wear, or imprecise manufacturing that a plain switch shrugs off is now enough to leave the knob ambiguously between two adjacent marks. Nothing about the dimmer is "more broken" than the switch — it's just been asked to make ten reliable distinctions using the same physical travel that the switch only had to split in two.
Example 2 — a real decimal counterexample: ENIAC
Binary isn't inevitable — it's just favored once you account for cost and reliability. ENIAC (1945), one of the first electronic general-purpose computers, is a genuine historical counterexample: it worked internally in decimal, using a ring of ten vacuum-tube states per digit instead of a handful of two-state stages. It worked, and it's proof decimal computing is possible, not a myth. But it paid the trade-off this lesson describes: representing one decimal digit that way costs meaningfully more hardware than representing one binary digit does, because ten reliably-distinguishable states just take more circuitry to build than two. As electronics matured and machines needed to pack in far more digits at lower cost, that trade-off tipped decisively toward binary — which is why virtually every machine this course's fluency is meant to support (vintage drum machines like the LGP-30 among them) is binary internally, even in cases where addresses or output get printed for humans in decimal or hex instead (a separate topic, for a later lesson).
Example 3 — it's not about what numbers a computer can represent
A ten-state machine like ENIAC can represent exactly the same decimal numbers a person writes on paper, digit for digit. A two-state machine can represent every one of those same numbers too — it just needs a different counting system to do it (binary place value, which is exactly what lesson 2 teaches). Neither machine is limited in what numbers it can represent. The only thing that differs is how expensive and reliable it is to build the hardware that stores and moves those digits. That distinction — between "what can be represented" and "what's cheap to build reliably" — is the one this whole lesson rests on.
Exercises
Exercise 1. In your own words: why is it cheaper and more reliable to build hardware that only has to distinguish two states (on/off) than hardware that has to reliably distinguish ten states (0-9), given the same underlying physical range to work with?
Exercise 2. ENIAC really did compute in decimal. Does that mean the "two states are more reliable and cheaper" reasoning in this lesson is wrong? If not, what does ENIAC's design actually show instead?
Exercise 3. A classmate says: "Computers use binary because 0 and 1 are the only numbers computers are able to understand." What's wrong with this claim, based on this lesson?
Show Answer Key
1. With only two states to tell apart, you can leave a wide, generous gap between "counts as off" and "counts as on," so noise, aging, heat, and manufacturing variation all have a lot of room to move around in before they'd ever cause a misread. Packing ten states into that same physical range shrinks the gap between each adjacent pair of states to a tenth the size, so the same small disturbance that a two-state design shrugs off is now enough to flip a correct reading into a wrong one.
2. No — ENIAC shows decimal computing is genuinely possible, not that the reliability trade-off is false. It shows the trade-off being paid directly: building a reliable ten-state digit took meaningfully more hardware than a two-state digit needs. Binary became the near-universal choice not because decimal doesn't work, but because as machines needed to scale up, decimal's extra hardware cost per digit stopped being worth paying.
3. The claim confuses "what a computer can represent" with "what's cheap and reliable to build." A computer built from ten-state components — ENIAC, for instance — can represent ordinary decimal numbers directly, no translation needed. Binary isn't a ceiling on what a computer can "understand"; it's an engineering choice about which physical states are reliably distinguishable at low cost. Lesson 2 builds directly on this: binary place value works exactly like decimal place value, just with two digits available at each position instead of ten — nothing about it limits which numbers can be represented.
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