# Abacus

Calculating Machines --- Abacus --- Napier's bones --- Slide Rule --- Logarithms --- Calculator

Many of the early number systems were hard for doing even simple arithmetic. So people developed a machine to do it for them. This started as stones in lines dawn in the sand. In fact, the word 'calculate' comes from the Latin word for 'stone', calculus. Eventually people developed the abacus. There are different types of abacus, so we will start with the simplest. Every bar has nine beads, and zero is when all the beads are at the top. The abacus has to be flat on a table, or all the beads would slid to the bottom, of course. But on this page, I will talk about 'pushing up' or 'pushing down' beads, meaning pushing them to the top or bottom of the screen.

### Enter number to see it on an abacus

Enter a number from 1 to 9999999 to see it on a simple abacus, or enter a number to count with.

Enter number:         every

### Interactive simple abacus

 Moved beads are       green blue red purple yellow brown -- Choose -- enter a number simple add simple subtract harder add harder subtract

An abacus uses a number of beads to represent a number, so it is a unary system. But a number of beads in one column are a different number to the same number in a different column, so it is a positional system. It doesn't really have a zero. If there is no value in one column, then there are no beads there.

### Eastern abacus

The simple abacus has ten beads per column. It isn't really used any more for calculation, although children sometimes use them to learn about numbers. Abacuses are still used in the Far East, but they look more like the abacus below.

The zero position is for all beads to be away from the central bar, as the beads on the left are. The top two beads represent five each, and the bottom beads represent one. The units column has a single 'one' bead and no 'five' beads, so this is one. The tens column has one 'five' bead and two 'one beads, representing 70. The hundreds has a 'five' bead alone, so that is 500. Then there is 3000 and 60,000. So the total number is 63,571.

This sort of abacus is easier to use, as the human eye finds it a lot easier to detect five beads or less, rather than larger numbers up to ten. You can quickly see the difference between 7 (a 'five' and two 'one's) and 8 (a 'five' and three 'one's), but 7 and 8 look similar on the simple abacus. You can see that the Romans would like this sort of abacus, as they had a symbol for five as well as a symbol for one. You may wonder why there are two fives as well as five ones, allowing a value up to fifteen in a single column. It's for much the same reason as the simple abacus having ten beads in a column. It allows you to store a number before having to carry it.

Below is an abacus of this type for you to play with. Click on the beads to move them.