pozorvlak | Counting in hexadecimal on your fingers

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Counting in hexadecimal on your fingers

A simple and occasionally handy trick which deserves to be better known.

Use your thumb as a pointer, and your finger joints and fingertips to represent the numbers. Thus:

Thumb pointing to base of index finger = 0
Thumb pointing to first joint of index finger = 1
Thumb pointing to second joint of index finger = 2
Thumb pointing to tip of index finger = 3
Thumb pointing to base of middle finger = 4
...
Thumb pointing to tip of little finger = F = 15

By using both hands, you can either have a counter with two hex digits (so you can count from 0 to 255), or two separate counters. You can use the same trick to count in base 12: ignore the fingertips, and just count on the joints. A nice side-effect of counting like this (as I discovered this afternoon) is that to casual observers you look like you're meditating: hold your hands palm upwards and stare at something for the full effect.

I learned this trick from an early chapter of Georges Ifrah's monumental Universal History of Numbers, the bulk of which has sat accusingly unread on my bookshelves since roughly 2002. While it looks fascinating, it's also about six inches thick (it's spread over three volumes), and thus is rather intimidating. The trick was listed as one of the ways in which pre-literate peoples count: the general rule is "by enumerating parts of their bodies in a predefined sequence", but the number and sequence of the parts varies from people to people (though less than you'd think). Base sixteen isn't as common a number base as 10 or 12, but it's far from unknown. Another interesting titbit from the book was the list of independent reinventions of "Roman" numbers: it seems that they're essentially the obvious way of counting using notches on a stick after "one notch per item" becomes unwieldy.

[Totally confused by this entry? Hexadecimal notation (or base 16) is a way of writing numbers down. In ordinary decimal notation, each column describes numbers ten times the size of the numbers in the column to its right; the sequence is ... thousands, hundreds, tens, units, tenths, hundredths, ... . In hexadecimal, each column describes numbers sixteen times the size of the numbers in the column to its right. This has all sorts of uses in computing and electronics. For more, see here.]

Edit: Reddit thread. And it seems I was totally wrong in thinking this technique was confined to preliterate people - it's extremely common throughout the Indian subcontinent, and probably further afield! I do like it when I learn something new from comments on a blog post. See the comments below for more finger-counting techniques (and yes, I already know about the sodding binary technique, I just choose not to use it because it's extremely uncomfortable for me. Happy? :-) ).

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Apparently such finger-counting methods are also used in prayer. So be careful; it might make you look religious. ;)

why? is being religious bad?

depends on how crazy you are

Yes.

A simple and occasionally handy trick which deserves to be better known.
Actually, this is how I learned to count on my fingers. It's common in South Asia -- seeing

shuripentu's link above makes me wonder if it's not a more general Muslim thing.

This guy (http://reddit.com/r/programming/info/6lrt2/comments/c047mqv) reports it also being used in India for those repeating mantras - so presumably among Hindus and Buddhists?

I imagine, if it's used for Hindu mantras and such as well, that it's a more general cultural thing :-) the subcontinent is surprisingly homogeneous in some ways!

Which base did you count in?

Joint to tip of each finger -- base 16 -- though it wasn't until I learned to geek that I realized how cool it was to be counting in hex :-)

What exactly do you mean by 'Roman' numerals? I think there are pretty much three systems that I have come across;
i) 'Counting' notation (count symbols for given numbers, e.g. Egyptian, Roman)
ii) Quasi-place notation (different symbols for 1,2,3...10,20,30...100,200,300)
iii) True place notation (ours!)

Do you mean the first, or including more of the details which I would consider to be specific to 'Roman' numbers - i.e. symbols representing [1/5]*10^x...

The (I, V, X) subset of (i), including the symbols used. L, D, C and M may have been unique to the Romans - given that they're abbreviations for Latin words, probably so. But then, it's been a long time since I read the book, and I can't be arsed to walk to the other end of the house to get it :-)

Has this post been mirrored somewhere? Its seems that you're getting a lot of quite lame anonymous comments...

Some idiot posted it to Reddit (http://reddit.com/r/programming/info/6lrt2/comments/), where it's been on the front page of the programming community for the last 18 hours or so, and where it briefly made the front page of the main site.

Most of the comments have been fine, and even educational, though the flood of "you should totally count in binary!!!11!!0011!010101!" comments has been a bit irritating.

By the way, if you're not familiar with Reddit, I strongly recommend that you stay away. It's a social news aggregator that's crack-like in its addictiveness. Yes, you'll learn interesting stuff and meet interesting people, but you'll also encounter a lot of angry trolls and waste huge swathes of time.

You can also count in binary on your fingers. Finger up = 1, finger down = 0. Be careful of the number four, though

Yep. I find that quite uncomfortable, though.

SWEET, love that trick. And much needed, ever since my attempt of counting in constants was a flop. (http://mozey.wordpress.com/2008/03/28/euler-phi-e-pi/) People just did'nt think that it was as cool as i thought!.

Hehe. Though I think you should read my post about Euler's equation (http://pozorvlak.livejournal.com/40478.html) :-)

The first 5 are fairly obvious
0 = Closed Fist
1 = Thumb
2 = Th + Index
3 = Th + Index + middle
4 = Th + index + middle + ring
5 = Th + index + middle + ring + pinky

the sequence continues the opposite direction by changing the next digit in sequence.

6 = Th + index + middle + ____ + pinky
7 = Th + index + ______ + ____ + pinky
8 = Th + _____ + ______ + ____ + pinky (Hang loose)
9 = __ + _____ + ______ + ____ + pinky

then keep going

10= __ + index + ______ + ____ + pinky (Metal Rules)
11= __ + index + middle + ____ + pinky
12= __ + index + middle + ring + pinky
13= __ + index + middle + ring + _____
14= __ + index + middle + ____ + _____
15= __ + index + ______ + ____ + _____

Two hands does 256.
And, it is viewable from a distance unlike counting the joints on each finger.

4 = Th + index + middle + ring

Are you saying you can actually do this??

Don't see why not? Th + index + ___ + ring [+ pinky], however, I simply can't do...

The rules around this method seem non-intuitive to me, compared to linearly counting up your joints. But I am biased :-)

I guess my pinky and ring are too connected to each other??

I can only do Thmb + Indx + Midl + Ring + ___ on my left hand (I'm right-handed). My right hand just looks deformed when I try that.

Interestingly, my left Pnky bends ever so slightly when I do Thmb + Indx + Midl + ___ + Pnky, but my right one is straigh.

You can go 4 times higher with binary. I've done this while counting paces, with the hands behind my back. It's easy, and if you ever "lose count", your most significant digits aren't moving often anyway and will tell you roughly where you were.

Yes, I much prefer counting in binary on my fingers, it's easier for me, and like you said, easier to keep track of where your fingers are.

I'm getting irritated now. Yes, I know about counting in binary on your fingers, and even if I didn't, you'd be the third person to tell me today. I find it uncomfortable, less intuitive, and less interesting than the hex trick.

Getting a single digit up to 15 isn't really counting 'in hex' -- it's not a positional number system at all. Compare with the 'counting binary on your fingers' where one hand gets you up to 31, resetting your thumb every time.

Getting two hex digits up to 255 is, however, definitely counting in hex.

With a good chance that I'm stating the obvious:
Use only two fingers for 8-based, i.e., octal.

Anyway, cool as hell!

Worth pointing out :-)

How bout Trinary?

Joints of your index fingers? That only gets you two digits, though. You could try something like the binary trick, with three separate positions for your fingers. Good luck not losing your place.

lol

The Hindustani rhythm teen-tal has been counted this way for centuries.

I never claimed it was original...

But in general, I'm surprised how widespread this trick is. I have learned something. Thanks, everybody!

I think you meant "tidbit" instead of "titbit." Unless you're trying an interesting new method of counting in trinary... :D

The Internet != The USA. Titbit (http://www.askoxford.com/concise_oed/titbit) is much more common than tidbit over here.

No, I mean "titbit", which is how we say it in the UK. Trinary digits are usually called "trits", anyway :-)

Goodness, is there a breeze? It's a tittybit nipply in here...

what is this counting good for? I now can count from 0 to 15 (F) using my hand. what do you use it for? I can count that far already by using only my brain. This is confusing, can someone explain the actual usage?

Your brain has one less thing to keep track of. This is occasionally useful, even for smart people. The use case that prompted me to post this was the following: I was going through my Livejournal friends list, counting how many people on it were female and how many were male. I counted women on my left hand and men on my right: my brain then only had to remember how many times the counts had overflowed, and was otherwise free to concentrate on reading the names, assigning them to actual people, and remembering the sexes. The final counts were (I think) 43 and 39: I would surely have lost count several times if I'd done all the counting in my head, and using paper would have been tediously heavyweight.

But mainly, it's just cool. Pleasingly techie, and requiring no equipment beyond your own body.

I agreed with you

Counting in octal was always fun.
one, two ... seven, oct, octy-one, octy-two ... octy-seven, twoct, twocty-one, twocty-two ... twocty-seven, throct, throcty-one, etc up to sevocty-seven, octy-oct. (Decimal 64)

thats it, dude

omg.. good work, brother

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Counting in hexadecimal on your fingers

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binary

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I count in constants!

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Another Method

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255?/Hex? Binary = 1023

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Been done for centuries in counting Teen-Tal

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hehehehe

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I don't understand

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I should say

counting

thanks much

thank you

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