COMPVTER ROMANVS

Caesar has proclaimed Compvter Romanvs to be the official calcvlator of the Roman Empire. Yov now have at yovr disposal the latest in high technology to assist in all manner of nvmerical problems. Yes, whether yov're bvilding a road, designing an aqvadvct, or covnting yovr gladiators, Compvter Romanvs will make the job easier.

Yov can even vse it to convert barbaric nvmbers into proper Roman nvmerals. Yov can also learn abovt transforming dates into Roman covnting



Error Codes
From time to time, yov may notice a blinking nvmber in the calcvlator display; this is an error code cavsed by a barbarian performing an invalid operation. Here is a table of the error codes along with their meanings:
I Indicates an overflow condition. An operation has resvlted in a qvantity greater than the largest nvmber that exists (Max roman numeral).
II Indicates an vnderflow condition. An operation has resvlted in a qvantity smaller than the smallest nvmber that exists (I).
III Indicates that the vser has entered an invalid seqvence of nvmerals.
To clear the error, press the key with the small "c" on it. Repeated errors will resvlt in the vser being thrown to the lions.




Nvmeral Valves
The following table gives the valves of the variovs nvmerals. When a bar appears above a nvmeral, its valve is increased a thovsandfold.


Nvmeral Valve With Bar
I One (Invalid)
V Five Five thovsand
X Ten Ten thovsand
L Fifty Fifty thovsand
C One hvndred One hvndred thovsand
D Five hvndred Five hvndred thovsand
M One thovsand One million




Nvmeral Syntax
Vse the following gvidelines to constrvct and evalvate qvantites expressed in Roman Nvmerals:


I Generally speaking, smaller nvmerals follow larger nvmerals (see rvle III below). In svch cases, add vp the valves of the nvmerals to determine the qvantity represented.
II Nvmerals which are powers of ten (I, X, C, etc.) can be repeated vp to three times in a row; other nvmerals cannot be repeated.
III In certain cases, a smaller nvmeral may precede a larger one. Evalvate these expressions by svbtracting the smaller nvmeral from the larger one. A smaller nvmeral can be placed before a larger one only if ALL of the following conditions are met:
-- The smaller nvmeral mvst be a power of ten.
-- The smaller nvmeral mvst be either one-fifth or one-tenth the valve of the larger one.
-- The smaller nvmeral mvst either be the first nvmeral in the expression, or be preceded by a nvmeral of at least ten times its valve.
-- If another nvmeral follows the larger nvmeral, it mvst be smaller than the one that precedes the larger nvmeral.



Nvmeral Conversion
Vse the following gvidelines to convert Arabic nvmerals into Roman Nvmerals:

Example: Converting 13,692 into

-- Express the nvmber as a svm of the nvmbers from the Nvmerical Valves table:

13,692 = 10,000 + 1,000 + 1,000 + 1,000 + 500 + 100 + 50 + 10 + 10 +10 + 10 + 1 + 1

-- Enter the svm into the Compvter, vsing the Nvmerical Valves table for conversion:

-- Observe the answer!



Roman Dates in Jvlian calendar
Vse the following gvidelines to convert Western (Gregorian) dates into Roman Dates. It may amvse yov to convert yovr birthday or other holiday.

-- The names of the months are: martivs, aprilis, maivs, ivnvs, ivlivs, avgvstvs, september, october, november, december, ianvarivs and febrvarivs; martivs is the first month of the Roman year.

-- The nvmber of days in each month is the same as in Western calendar, bvt Roman calendar does have leap years on years 200, 300, 500, 600, 700, 900, 1000, 1100, 1300, 1400, 1500, 1700, 1800, 1900, 2100, 2200 whereas Gregorian calendar does not. As a resvlt, the Jvlian (Roman) date is, dvring this centvry, 13 days behind the Gregorian date.

Example: September 19th in Gregorian corresponds to September 6th in Jvlian

-- The three most important days in each month are:

Kalendis - the first day

Nonis - the seventh day in martivs, maivs, ivlivs, and october and the fifth day in other months,

Idibvs - eight days after the Nonis, either on the thirteens or on the fifteenth day of the month.

--All the other days are named after how many days they are before the next of these three, covnting inclvsively (that is, yov covnt the day yov start from).

Examples: Avgvst 9th  in Jvlian is written as ante diem V idvs avgvstvs

March 2nd is ante diem VI nonas martivs

--The day immediately before the Kalendis, Nonis or Idibvs is called pridie rather than given a nvmber.

Example: March  31 is pridie kalendas aprilis

-- In leap years (as given by the Jvlian calendar), the name ante diem VI kalendas martivs is given to both the 24th and the 25th of Febrvary.

-- The years are covnted from the fovndation of The City (Rome, of covrse), or ab vrbe condita which occvrred in 753 BC. The year 753 BC is therefore nvmbered I, 1 BC is DCCLIII (753) and 1 AD is DCCLIV (754), so yov have to add 753 to convert Gregorian dates into Jvlian dates.

Examples:

2000 AD is MMDCCLIII (2753)

September 25, 1972 in Gregorian is pridie idvs september MMDCXXV in Jvlian

Febrvary 2, 1854 is ante diem XII kalendas febrvarivs MMDCVII (observe that only 12 days are svbtracted for the difference in leap years)



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