# Binary wrist watch ๐ค

A couple of weeks back I bought a binary watch (wellโฆ binary-coded duodecimal/sexagesimal) on a whim. It was cheap and ugly but I figured it would be kind of fun to test myself a little. A quick mental puzzle whenever I want to know the time. ๐

Binary wrist watch (Amazon.de)

Interestingly, while telling the time was somewhat cumbersome at first, it is rapidly getting easier. I have realised that I am starting to simply memorise quite a few positions, so that I can often read the time at a glance. I have also begun to notice patterns I had not really thought about or considered before wearing a watch like this. For example, any time you have a combination and it moves one place to the left it is (obviously) doubling. Since 000011 is 3, 000110 is therefore 6 and 001100 is 12. That means that as you learn basic patterns (when combining smaller numbers), you can use them to quickly understand bigger combinations that look the same.

A very helpful one is that anytime you have two lights with a space in between them, they will be multiples of 5/10, e.g.

0 0 0 1 0 1 4 1 = 05 0 0 1 0 1 0 8 2 = 10 0 1 0 1 0 0 16 4 = 20 1 0 1 0 0 0 32 8 = 40

Those specific combos (above) are handy as they often simplify quickly calculating stuff. It is easy to do maths with 10s (and 5). So when looking at a sequence it helps to calculate these positions first. Initially 011110 can appear to lot of work to do in your head but then you realise it is just the middle two patterns (above) overlapping (10 + 20) and thus 30.

You could also approach understanding 011110 a different way. Another pattern that becomes rapidly obvious is that if all the numerals to the right of a position are 1 then they add up to one less than that numeral's position. Since 010000 is 16, 001111 must be 15. Move 001111 left by one position (to 011110) and again you realise that it is 30 because of the doubling I mentioned previously.

With enough time I suspect that reading this watch might not be much more work than reading a normal digital or analog watch face. Still the process of getting there is fun!

P.S. Whilst researching binary watches (looking for something a little less ugly), I made a couple of interesting finds:

Wikipedia article on binary clocks

Binary clock at St. Gallen train station in Switzerland

A small home binary clock that looks like a Parisian Haussmannian building

โ

/gemlog/