Number Bases: Octal & Mixed

Binary, hex and decimal. The way computers count.

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Binary to Decimal Decimal to Binary Hexadecimal Octal & Mixed

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How Number Bases: Octal & Mixed works

We count in tens for the accidental reason that we have ten fingers. Computers count in twos because a switch is either on or off. Hexadecimal exists because sixteen is a power of two and four binary digits fit neatly into one hex digit.

None of that is difficult once you see that a base is just a set of column values. In base ten the columns are 1, 10, 100. In binary they are 1, 2, 4, 8, 16. Everything else follows.

This version: Base eight and mixed conversions. Your best score is saved in this browser, so you can come back and try to beat it. Nothing is uploaded and no sign-up is needed.

Frequently asked questions

Do I need this if I am not a programmer?

Not strictly, but it is the clearest possible demonstration that our number system is a choice rather than a law of nature. Most people find that genuinely interesting once it clicks.

What is the quickest way to read binary?

Learn the column values 1, 2, 4, 8, 16, 32, 64, 128 and add up the columns with a 1 in them. 1011 is 8 + 0 + 2 + 1, which is 11.

Why does hexadecimal use letters?

Because base sixteen needs sixteen digits and we only have ten. A to F cover the values ten to fifteen.

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