It was during the Ancient Times from the period of c. 300 B.C to c. 500 A.D that the Roman Abacus was invented. It was properly termed as Roman hand abacus.
Development of Roman Abacus
There was no recorded discovery of the existence of the Roman hand abacus or even a specimen that would prove that indeed there was such as Roman hand abacus. However, language one of the most reliable sources of past culture or history would prove to the fact that indeed there was such a counting device Roman hand abacus.
It would confirm as such that the Greek has psephoi its Roman counterpart is calculi. In Latin the word calx would mean pebble. Thus, a calculus means little stones that would be used as counters. It served as a proof that Romans had an actual counting board which they will use this calculi as counters. This counting board was the Roman hand abacus.
Structure of Roman Abacus
The Roman Abacus was made of metal plate and this was where the beads ran in slots. The size of the abacus was such that it can fit into the pocket of a modern shirt. It consists of seven longer which had up to four beads in each and seven shorter grooves which had only one bead that was used for the whole number counting. The rightmost two grooves were used for fractional counting.
The Roman hand abacus had a lower groove which represents units and the beads in the upper grooves were in fives such that five units, five tens and so on. The groove values were marked by roman numerals. This was designed to bi-quinary coded decimal system.
Computation using Roman Abacus
Computations through the use of Roman Hand Abacus made by using the beads and slid them up and down to the grooves in order to denote the value of each of the column.
The upper slots of the Roman Hand Abacus contained a single bead while the lower slots contained four beads but there is an exception that is the two rightmost columns. These two slots are used for a mixed-base math which is unique to the Roman hand abacus.
The longer slots which contained five beads are used for counting of 1/12th of a whole unit. This makes the abacus very useful to the Romans in terms of measures and currency.
The rightmost slots were used to enumerate fractions of an uncia. These were from the top to the bottom, such as 1/2s, 1/4s and 1/12s of an uncia.
Absence of Zero and Negative Numbers in Roman Abacus
In a counting board or abacus the rows or columns represent zero. The Romans used Roman numerals in order to record results. Roman numerals were all positive so there was no need for a zero notation. The Romans already knew the presence of the concept of zero incorporated in any place value, column or row.
The Roman merchants already knew that there was a need to learn and understand the concept of negative numbers in order to compare and analyze their loans as to their investments and their liabilities as to their assets.
Even if the Roman hand abacus only represents positive numerals still the Romans used the concept of zero and negative numbers in terms of trade.