Binary Fingermath

There is another way of doing math on your fingers, which gives you a much greater range of numbers, and which makes multiplication particularly easy. It’s a bit more work to get used to than the finger abacus, but it has a lot less limitations. Someone in the comments of the finger-abacus post mentioned that they do something similar.
The methods for binary fingermath that I’ll describe are my own creation; so if you think they’re ridiculous, the blame is entirely mine. I know other people have come up with similar things, but this is my own personal variant.

The idea is to use your fingers in binary: the thumb is 1, the pointer is 2, middle finger 4, ring finger 8, and pinky 16. With this, you can get to 31 on one hand, or 1023 with both. So, here’s a diagram of a few different numbers on the right hand:

We’ll start with the simplest version of addition – this can be done on one hand, but it’s easiest to use two hands, with one as a placekeeper. The basic algorithm is:
1. Put one number on each hand in binary.
2. Go to the lowest raised finger on the left hand:
1. Lower that finger on the left hand.
2. Add one starting at the same finger on the right hand:
1. If the finger is lowered, just raise it.
2. If the finger is *raised*, then lower it, and add one starting
at the next finger.
3. Repeat step 2 until the right hand is zero.
So, here’s an example of finger-binary addition:

For larger numbers, I like to use a stack of pennies. Lay out ten pennies in front of you. Put one number on your hands – do the other number using the pennies – push pennies away from you for a one, towards you for a zero. The algorithm remains the same – except that now you can do additions up to 1000.
You can also do binary multiplication on your fingers, but that’s a topic for tomorrow.

0 thoughts on “Binary Fingermath”

1. Spook

Ah this is a classic. I figured this out when I learned what binary was, but didn’t know about carrying numbers at that age.
Terribly handy to be able to bit-shift on your fingers though.

2. Rob Knop

Wow. This is why you are #1 nerd, and I’m only #2 nerd.
I count in binary on my fingers all the time. I started doing it in college, and quickly decided not to use the tumb. (Reason: it’s kinda hard to move some fingers up and down independently, and it’s useful to have the thumb as a tool for holding fingers down.) (Secondary reason: then I have 8 fingers, which is one byte, and I’m a computer nerd.)
I use the little finger as bit 0, becuase it is, after all, the least significant digit…. That does preserve the middle finger as 4, so if I’m annoyed at somebody, I can think “36” in my head, and I’ll know what I’m thinking.
It’s often been convenient to be able to count to 255 on my fingers, and I do use this in real life reasonably often. But I’ve never done bitshifting and arithmetic on my fingers before….
-Rob

3. Marc

If you just want to count on your fingers, base 6 is nice: digits on your right hand, tens on your left.
You can only count up to 35, which is less then 1023, but it is easier on the fingers then binary (where 8 is pain in the … hand)

4. Michele

I wish I had known about this when I was younger. When I was a child my mother never let me use my fingers to count. As I got older, I wasn’t allowed to use a calculator either. I could use pencil and paper or learn to use the abacus (which I never did – too lazy).

5. Xanthir, FCD

Hmm. I’ve never done multiplication on my fingers, but I assume it would be a direct translation from the standard binary multiplication algorithms, same as adding is here – a combination of bitshifting and adding.

6. jerith

I haven’t really done much binary arithmetic on my fingers, but I count bars of rests in binary. It helps that they often come in some convenient combination of powers of two. At one point I had half the trombone section in my band doing it — most of them didn’t even know what binary /was/…