Calculator

Perhaps the earliest calculating machine was the Babylonian rod numerals. Not only was it a notational device, but administrators carried rods of bamboo, ivory, or iron in bags to help with their calculations. Rod numerals used nine digits (Figure 1).

The next invention in counting machines was the abacus. A counting board dating from approximately 500 B.C. now resides in the National Museum in Athens. It is not an abacus, but the precursor of the abacus. Oriental cultures have documents discussing the abacus (the Chinese call it a suan phan and the Japanese the soroban) as early as the 1500s A.D.; however, they were using the abacus at least a thousand years earlier. While experts disagree on the origin of the name (from either the Semitic abq, or dust, or the Greek abax, or sand tray), they do agree the word is based upon the idea of a sand tray which was used for counting.

A simple abacus has rows (or wires) and each row has ten beads. Each row represents a unit ten greater than the previous. Thus, the first stands for units of one; the second, units of ten; the third, units of hundred; and so on. The appropriate number of beads are moved from left to right on the wire representing the unit. When all ten beads on a row have been moved, they are returned to their original place and one bead on the next row is moved. The soroban divides the wires into two unequal parts. The beads along the lower, or larger, part represent units, tens, hundreds, and so on. The bead at the top represent five, fifty, five hundred, and so on. These beads are stored away from the central divider, and as needed are moved toward it.

Finger reckoning must not be ignored as a basic calculator. Nicolaus Rhabda of Smyrna and the Venerable Bede (both of the eighth century A.D.) wrote, in detail, how this system using both hands could represent numbers up to one million. The numbers from 1 to 99 are created by the left and the numbers from 100 to 9,900 by the right hand. By bending the fingers at their various joints and using the index finger and thumb to represent the multiples of ten, combinations of numbers can be represented. Similar systems were devised much earlier than the eighth century, probably by merchants and traders who could not speak each other's languages but needed a system to communicate: their fingers. Multiplication using the fingers came much later; well into the fifteenth century such complex issues, as multiplication, were left to university students, who were forced to learn a different finger reckoning system to accommodate multiplication.