Binary decimals?

So I love a good xkcd as much as the next nerd, but this one got me thinking a little too much:

To wit, what is the probability? I mean, part of that is the assessment of the girl's GI (Geek Index), but then also how does one break up the "number line" between 1 and 10 in binary? I mean, in decimal, you can have 1.0, 1.1, 1.2 ... 1.9, 2.0, which one can also write as 1 + a fraction: 1 + 0/10, 1 + 1/10 .. 1 + 10/10.

Those same fractions, in binary, become 1 + 0/10, 1 + 1/10, and 1 + 10/10 = 1 + 1 = 10, so it seems as though there is one fraction "halfway" between 1 and 10, with the option for infinite continued bisection. But is that a notational trick? I really have no idea what "1.5" in binary means.

P.S. I'm sure the internet has an answer, but at this point I don't feel like looking. Or rather, it's kinda fun remaining ignorant and spending a couple minutes pretending Google doesn't exist.

  

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Michael

"O Whisky! soul o' plays and pranks! Accept a bardie's gratfu' thanks! When wanting thee, what tuneless cranks Are my poor verses! Thou comes-they rattle in their ranks, At ither's a-s!" Robert Burns - "Scotch Drink" 1785

2 thoughts on “Binary decimals?”

  1. What is 1.5 in binary. Hmm. Yeah, I don't think it exists. Negatives don't exist either. Well, not in the ADCs that we use. Not that you can't express them, but it takes more than one bit. Actually, to think about it, that's the difference between bits and bytes isn't it. A bit is the yes-no binary and the byte is a character referenced by those eight bits.

  2. Yeah, I think that's a key distinction (bit/byte), and it's not a terribly functional concept, but based on the fractional notation above it seems as though 1 + 1/10(b) is a perfectly valid notional construct?

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