Reading a binary watch, tips & tricks
=====================================
[7 minute read]
I first learnt binary as a kid at school and on a few (admittedly
rare) occasions it has been useful to know it for my day job (I work
in IT). However these days, it is primarily just something I use to
read my binary watch. ;)
~ Binary wrist watch:
gopher://sdf.org/0/users/r0/phlog/2021-11-23_Binary_wrist_watch.txt
What I have found after wearing that watch on and off over a couple of
years is that it rapidly got easier to read, at least for the range of
numbers found on clocks ('1-59').
How to read a binary watch
--------------------------
On my watch, the top row shows the current hour. The LEDs here
represent '8', '4', '2' and '1' (read from left to right). The bottom
row displays the current minute and the LEDs represent '32', '16',
'8', '4', '2' and '1'. In short, you just need to add up all the lit
LEDs, to find the decimal numbers representing the hour and minute.
Once you have the basics down, here are a handful of tricks and
shortcuts that are useful for quickly reading a binary watch.
[i] [In this guide I will represent lit LEDs as 1 and unlit LEDs as 0.
For the most part I will just list the right-most positions (assume
the rest are unlit).]
Numbers that end with 0 are even
--------------------------------
Or put another way, numbers that end with 1 are odd.
1 = 1
10 = 2
11 = 3
100 = 4
Most people will see this immediately but it is worth keeping this in
mind as it is handy as a quick check that there might be something
wrong with your calculation, i.e. if the number you calculate is even
but what you see ends with 1... you did it wrong! ;)
Doubling patterns
-----------------
This is also obvious when you really think about it but something that
I had not noticed until I started using the watch. The point here is
that all patterns of smaller numbers double when moving one step to
the left.
Consider a number like 11. That is fairly easy to read as '3'. Once
you understand this any number containing that pattern is also pretty
obvious.
110 = 6
1100 = 12
11000 = 24
110000 = 48
Similarly 101 is '5' and so
1010 = 10
10100 = 20
101000 = 40
111 is '7' and thus
1110 = 14
11100 = 28
111000 = 56
Since 1001 is '9'
10010 = 18
100100 = 36
[i] [If you recall the shortest version of a pattern, you can just
double it as it moves left by each position.]
Memorise frequently used patterns/numbers
-----------------------------------------
In addition to quickly memorising many of the small patterns from use
(and their multiples), you might want to remember commonly used times,
e.g 1111 [15], 11110 [30] and 101101 [45] (for the half and quarters
of the hour). That last one is also interesting looking, so easy to
recall.
Always work out the minutes first
---------------------------------
[i] [More often than not you know the hour already, additionally it is
usually a smaller number.]
Many LED based binary watches give you a few seconds (after a
keypress) to calculate the time before all the LEDs dim. If you work
out the minute first, that will often be enough. And with the more
limited number of possible times for the hour, you may read it at a
glance anyway (as you will soon have all those positions memorised).
One less
--------
Numbers such '3', '7', '15', '31' are really easy to spot because they
just solid blocks of '1s'.
11 = 3
111 = 7
1111 = 15
11111 = 31
Compare those to the next number in sequence to see what is going on.
100 = 4
011 = 3
1000 = 8
0111 = 7
10000 = 16
01111 = 15
100000 = 32
011111 = 31
The number immediately proceeding a major number like '2', '4', '8',
etc. will have a stack of 1s to the right.
Another way to think of that is that you just invert the numbers from
the right-most 1 to decrease the number by '1'.
101100 = 44
101011 = 43
Calculate unknown numbers using ones you already know
-----------------------------------------------------
Take a number like 110111. Initially one might work that out with lots
of small additions.
1 1 0 1 1 0
32 + 16 + 0 + 4 + 2 + 1 = 55
Not hard but it takes a little time to do in your head. I would tend
to look at this other ways. There are two overlapping patterns I
instantly recognise here, 110000 is '48' and 000111 is '7', so '48+7'
= '55'. Or perhaps, I would just count back from a higher number I
recognise. I know 111000 is '56'. 110111 is one less (if you invert
the numbers from the right-most 1).
If you look at binary numbers frequently and already know 111000 (I
mentioned it above), you can spot that last one in an instant.
Final thoughts
--------------
These are just a few of the tricks I have picked up to show how you
can interpret binary in decimal terms more easily (without calculating
every number). For the most part I can now read my binary watch pretty
quickly. Often at a glance and in the worst case, usually within a
couple of seconds. No that is not as fast as a normal digital or
analog but quick enough to make it useable and useful. I also suspect
that if I used it more (I rotate through a bunch of odd watches) I
could reliably match the speed of (accurately) reading an analog
clock. You do after all find yourself just memorising a bunch of
positions (through regular use), so the amount of calculation you have
to do, rapidly drops.
I will add however that there is one problem that occasionally catches
me out with binary watches that use LEDs specifically. In pitch black
it can sometimes be hard to pick out the positions of the off state
LEDs. Thus a number like 11 can look similar to 110 (they both just
look like two lit LEDs that are next to each other). And that my
friends is how I once woke at 06:00 in the morning and started to make
coffee and prepare for the day, only to later realise it was actually
03:00! XD
* * *
[EDIT 2023-11-06 @14:06 +0100]
Bonus trick for approximation
-----------------------------
Here is another small trick that was quite handy when I first started
using the watch (and was much slower at calculation).
You can sort of use a binary watch for glancing approximation (similar
to how many use analog watches) if you only need to know roughly where
you are in the hour, rather than the absolute minute. This is usually
"good enough" for upcoming meetings or events, which tend to fall on
the hour or half hour.
The minute line is 6 LEDs long but you only need look at the left-most
two to do this. As an added bonus, if you have an event up coming you
will often already know the current hour anyway. In that case you can
ignore the hour line entirely and just focus on these first two LEDs
on the minute line.
If neither are lit you are within the first quarter of the hour.
00[…] = '0-15' mins
If only the right one is lit you are over the first quarter but most
likely not half way through the hour.
01[…] = '16-31' mins
If only the left one is lit you are over half way through the hour but
probably not into the last quarter (or only just!).
10[…] = '32-47' mins
If both are lit you are over the final quarter and most likely within
the last 10 minutes of the hour.
11[…] = '48-59' mins
[EDIT 2023-11-07 @09:04 +0100]
[i] [In the real world you will not see these two LEDs in isolation.
You will still have a vague awareness of the others, even if you do
not attempt to properly calculate them. More lights (particularly
those close to the two right-most LEDs) will give you a rough feeling
for how close you are to the crossover times.]
* * *
