Information converter
Convert information between bits, nats and hartleys, and see how many possibilities that much information pins down.
That's about the same as a byte. That much information picks one outcome out of about 256.
What it means
How much information is that?
This is Shannon information, not file size. A megabyte file may carry far less than eight million bits of actual information, which is why it compresses.
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Three things worth knowing
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n bits distinguishes 2ⁿ things
So 8 bits is 256 possibilities, and 60 bits is about 10¹⁸ — which is why a 60-bit password is hard to guess.
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Shannon, 1948
He defined information as the reduction in uncertainty, measured by a logarithm, and invented the word "bit" for its unit. Every codec and error-correcting code descends from that paper.
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Bits of information are not bits of storage
A file of a million zeros takes a megabyte of disk but carries almost no information. The gap between the two is exactly what compression removes.
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Background
About bits and nats
One bit is the information in a fair coin toss: it halves the possibilities. Eight bits distinguish 256 things, which is why a byte holds 256 values.
The unit is really a choice of logarithm base. Base 2 gives bits, base e gives nats — natural in mathematics — and base 10 gives hartleys, which is what Turing’s team called bans.