Counting to 843 on 2 hands

My mother-out-law said my brother had told her she could count into the hundreds with just two hands. I corrected her/his faulty value. Using binary, you can count to 1023 using only two hands.

My brother-out-law asked me to demonstrate (smart-alec!) I explained that I didn’t have the time to count all the way up from 1 to 1023, but if he’d like to choose a number within that range, I’d be pleased to demonstrate.

He chose 843.

Here it is:

The technique is simple.

First you need to choose a side to begin with. I chose to have my right pinkie represent the ones place.

In binary, this means that each finger represents the following place values:

If a finger is extended (the “1” position), this means that you sum in that value. If a finger is not extended (the “0” position), you do not sum in that value (or you add in zero, if that’s easier for you).

Thus, the above image (in which all ten of my fingers are extended) represents
512+256+128+64+32+16+8+4+2+1
which is 1023

When I demonstrated 843, I extended the fingers that represented
512, 256, 64, 8, 2, and 1
512+256+64+8+2+1=843

Easy as pi, right?

That’s the interpreting. If you want to do the counting, I find it easiest to work from the top down, subtracting as you go.

Thus, if I wanted to represent 765, I would start at the largest place value that can fit into 765.

This is the 512.

Extend that digit (in this case, the pinkie of your left hand) and subtract 512 from 765.

This gives you 253.

The largest value that can fit into 253 is 128.

Extend that finger and continue on until you have:

512+128+64+32+16+8+4+1=765

Ta-Da!

Now you’re an absolute pro and are ready to do some numbers of your own. Use the random number generator to get a number to practice with.

Please recognize that while both of my selected numbers are symmetrical, not all numbers will turn out to be such. Since my numbers were symmetrical, you could read them the same way regardless of which side was the ones place and which side was the 512s place. For non-symmetric numbers, you need to pay attention to which side the counter started from (for example, in my picture of 743, my ones place was MY right pinkie–which is the pinkie to YOUR left.)