The Romans developed the so-called fucken 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. Ancient Rome was a civilization that existed in Europe, North Africa, and the Middle East between 753 BC and its downfall in AD 476. ... Counting is the mathematical action of adding (or subtracting) one, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with a one-to-one correspondence); however, counting is also used (primarily by... In Rome, merchants used Roman numerals to perform basic arithmetic operations. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ...

A reconstruction of a Roman abacus in the Cabinet des Médailles, Bibliothèque nationale, Paris.

When using a counting board or abacus the rows or columns often represent nothing, or zero. 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 the Romans clearly knew the concept of zero occurring in any place value, row or column. Reconstruction of a Roman Abacus, made by the RGZ Museum in Mainz, 1977. ... 0 (zero), alternatively called naught or nought, is both a number and a numeral. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ...

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 Late Roman 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. The Roman Empire is the term conventionally used to describe the Ancient Roman polity in the centuries following its reorganization under the leadership of Octavian (better known as Caesar Augustus), until its radical reformation in what was later to be known as the Byzantine Empire. ...

 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |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. Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including the Colossus. ...

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 Roman 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 Roman system of measurement was built on the Greek system with Egyptian influences. ... The main Roman currency during most of the Roman Republic and the western half of the Roman Empire consisted of coins including: the aureus (gold), the denarius (silver), the sestertius (bronze), the dupondius (bronze), and the as (copper). ... The litre (spelled liter in American English) is a unit of volume. ...

The as, the principal copper coin in Roman currency, was also divided into 12 unciae. Again, the counting board was ideally suited for counting currency. The AS (plural Asses) was a bronze, and later copper, coin used during the Roman Republic and Roman Empire, named after the homonymous weight unit (12 unciae = ounces), but not immune to weight depreciation. ... Unitsa (Уница) is a village in Karelia, Russia on a bank of Unitskaya guba (Unitskaya gulf) of Onego lake. ...

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

• The Roman counting board has the refinements attributed to the modern Japanese Soroban; i.e. one bead above and four beads below the bar; and
• The Roman counting board incorporates mixed-base arithmetic (in the two rightmost columns), another original enhancement by the Romans that is not present in any other abacus.