The Ancient Rome developed the so-called Roman abacus, or rather a portable counting board, based on previous Greek counting boards. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of Roman arithmetic using Roman numerals.

When using a counting board or abacus the rows or columns often represent nothing, or 0 (number). Since the Romans used Roman numerals to record results, and since Roman numerals were all positive, there was no need for a zero notation. But Roman numeral#Zero occurring in any place value, row or column.

It may be also possible to infer that they were familiar with the concept of a negative number as Roman merchants needed to understand and manipulate liabilities against assets and loans versus investments.

=Layout=

The Roman Empire counting board shown here as a reconstruction contains seven longer and seven shorter grooves used for whole number counting, the former having up to four beads in each, and the latter having just one. The rightmost two groves were for fractional counting. The counting board was made of a metal plate where the beads ran in slots. The size was such that it could fit in a modern shirt pocket.

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |O| |O| |O| |O| |O| |O| |O| |O| MM CM XM M C X I 0 ~3 --- --- --- --- --- --- --- --- --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ) |O| |O| |O| |O| |O| |O| |O| |O| | | |O| |O| |O| |O| |O| |O| |O| |O| | | |O| |O| |O| |O| |O| |O| |O| |O| | | |O| |O| |O| |O| |O| |O| |O| |O| |O| 2 |0| |O| The diagram is based on the Roman abacus at the London Science Museum.

The leftmost seven rows are used in whole item arithmetic and the abacus can count up to ten million. The two rightmost slots where used to count fractions - 1/12ths and 1/3rds.

The lower groove marked I indicates units, X tens, and so on up to millions. The beads in the upper shorter grooves denote fives—five units, five tens, etc. , essentially in a bi-quinary coded decimal system.

Computations are made by means of beads which would probably have been slid up and down the grooves to indicate the value of each column.

The upper slots contained a single bead while the lower slots contained four beads, the only exceptions being the two rightmost columns, marked 0 and ~3.

The longer slot with five beads below the 0 position allowed for the counting of 1/12th of a whole unit making the counting board useful for Ancient Roman weights and measures and Roman currency. Many measures were aggregated by twelfths. Thus the Roman pound ( libra ), consisted of 12 ounces ( unciae ) (1 uncia = 28 grams). A measure of volume, congius , consisted of 12 heminae (1 hemina = 0.273 litres). The Roman foot ( pes ), was 12 inches ( unciae ) (1 uncia = 2.43 cm). The actus , the standard furrow length when plowing, was 120 pedes . There were however other measures in common use - for example the sextarius was two heminae . The As (coin) , the principal copper coin in Roman currency, was also divided into 12 unica. Again, the counting board was ideally suited for counting currency.

The rightmost position, the ~3, with only two beads, allowed the counting of 1/3rds of a whole unit. The use of this position is not clear but could be used to count partially full containers.

=Other facts=