Abacus- Please explain

[addams]

Hi.
I am from that non math place out there.

I saw an abacus, yesterday. Ten beads: Ten rows of beads.

My first thought was 10X10=100. I think that is wrong.

My second thought was 10! That is a much bigger number.

What is it really?

Millions?
Billion?
What?!?

No hurry. I may never see another abacus. I was surprised by that one.

[skullturf]

Do you just want to know how many beads there are? Or rather, the largest number one can count to using an abacus.

[Talith]

The largest number you could count to would be 11^9 = 2,357,947,691 if my understanding of how an abacus works is correct (essentially the (i+1)th row of n-1 beads is able to encode the ith n-ary digit of the integer).

[letterX]

It's unclear that aadams means that it has ten rows of ten beads. A more usual arrangement has a bar in the middle, and two beads above the bar and five below the bar. But there's any number of ways it can be set up.

I would have pointed you to the wikipedia page, but it turns out that it's oddly missing a detailed section about the actual use of the abacus. They can actually be used for more complex computations than just simple counting and addition. In particular, abaci with large numbers of wires had the extra columns for scratch space in various algorithms, not for counting astronomically large numbers.

I don't have my copy handy, but I seem to recall that "Mathematics: from the birth of numbers" (an excellent book) has a pretty extended discussion of their use.

[radams]

Normally, each bead on the rightmost wire represents 1, each bead on the wire to its left represents 10, each bead on the wire to its left represents 100, and so on. So, if you slid all ten beads up on all ten wires, that would represent the number 11,111,111,110. That's the largest number that the abacus can hold using the standard way of representing numbers on abaci.

Edit: Talith is right - you could theoretically get bigger numbers by using base 11.

[Sizik]

The largest number you could count to would be 11^9 = 2,357,947,691 if my understanding of how an abacus works is correct (essentially the (i+1)th row of n-1 beads is able to encode the ith n-ary digit of the integer).

Why the (i+1)th? Just put the first digit on the first row, second digit on the second, etc. to have 11^10 = 25,937,424,601 numbers (0 to 25,937,424,600).

[Talith]

Oh sorry, you're right. I was getting confused between the string which encodes the 11^9 bit, and the maximum you can count up to, given 9 bits to encode on.