Vn43.1 Binary Counting 7/7/77
At dinner this evening, the topic of counting on fingers arose.
After performing some finger sum, Miriam turned to Robby with 2 fingers
of her left hand raised and all the fingers of her right and asked:
Miriam Robby, how much is this?
Miriam No. It’s 25.
Tricked by this representation shift, Robby gave her an equally challenging
problem. Holding up both hands with 5 fingers extended on each:
Robby How much is this?
Miriam (Uncertain and not consistent) 10?
Robby No. 25. It’s 5 times 5. Get it?
With these fluid finger counting representations in the air, Gretchen
asked me to explain hexadecimal finger counting (I use such a procedure
to keep track of telephone ring counts so I can think of other things
while waiting for people to answer the telephone). Since Miriam had
just invented a second finger counting representation and Robby a third,
it seemed appropriate to show the children binary (Richard Feynmann
introduced this procedure to me in an informal chat when I was an under-
graduate). I held up three fingers of my right hand — pinky, fourth,
and index. “How much is this?” Knowing 3 was not my answer, Miriam
guessed that number. I believe Robby guessed 21. I said, “11. I have
a funny way of counting. Let me show you how.” I proceeded to count
from 1 to 31 on the five fingers of my right hand. When Miriam opined
that it sure was a funny way of counting, I told her there was some-
thing she used a lot that counted that funny way; could she guess what
it was? Miriam could not guess that computers count in binary. It
made no sense to her that they could add such a funny way and not take
forever to get a result.
Miriam, in order to trick Robby, invents (with one example only)
a 2 place finger counting representation. Robby counters with multi-
plication of the finger count of both hands. I show both a one hand,
five place binary counting representation.