Abacus in Various Number Systems

Abacus is probably the first of calculating devices. Encyclopædia Britannica traces the word abacus to the Phoenician abak (sand). American Heritage Dictionary points to the Greek word abax, which might have originated from Hebrew avak (dust). There is little doubt that Ancients used a flat surface with sand strewn evenly over it as a disposable tool for writing and counting. It's said that the great Archimedes was slain by a Roman soldier while concentrating on figures drawn in sand.
Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth. Each wire corresponded to a digit in a positional number system, commonly in base 10. A very curious state of affairs was mentioned by M. Gardner with a reference to K.Menninger. For more than 15 centuries the Greek and Romans and then Europeans in the Middle Ages and early Renaissance calculated on devices with authentic place-value system in which zero was represented by an empty line, wire or groove. Yet the written notations did not have a symbol for zero until it was borrowed by Arabs from Hindus and eventually introduced into Europe in 1202 by Leonardo Fibonacci of Piza in his Liber Abaci (The Book of Abacus).…