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The Problem
Write a program to convert Arabic numbers less
than 4000 to Roman numeral notation and display the result.
Background & Techniques
A good chance to review your Roman
numeral knowledge. A quick Web search will turn up lots of good links to
refresh you.
After playing with a few numbers I noticed that
the digits 1 through 9 have the same pattern whether they are in the
unit's, ten's, hundred's or thousand's position ( thousands up to MMM). The actual
characters are different but the pattern is the same.
| Units |
Tens |
Hundreds |
Thousands |
| I |
X |
C |
M |
| II |
XX |
CC |
MM |
| III |
XXX |
CCC |
MMM |
| IV |
XL |
CD |
MMMM |
| V |
L |
D |
MMMMM |
| VI |
LX |
DC |
MMMMMM |
| VII |
LXX |
DCC |
etc. |
| VIII |
LXXX |
DCCC |
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| IX |
XC |
CM |
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If we make a table
containing the seven characters I, V, X, L, C, D, M, notice that the units digit
uses
only the first 3 characters (I. V, X), the tens digit uses 3rd
through 5th characters (X, L, C), and the hundreds digit uses the 5th
through 7th (C, D, M). The program uses this
consistent pattern. Check the code to see how.
Addendum October 8,2005: Finally got
around to adding number conversions from Roman back to Arabic at a user's
request. A bit more complicated because there are many ways to form
invalid Roman numerals using valid letters. In fact a random
collection of digits 1 through 9 will always form a valid Arabic number, but a
random collection of letters I, V, X, L, C, D, M is quite unlikely to form a
valid Roman number.
The lack of a zero placeholder is another
problem. Our conversion code needs to identify that no numeral is
defined for a particular position so we can insert the missing
zero.
Running/Exploring the Program
Suggestions for further exploration
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Try allowing Arabic numbers up to 9999. Notice
that above 3999, the leading 'M's just keep increasing. (There are
some other conventions using lines over the M's or some such,
but they didn't seem to adapt very well to machine display.) |
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Implemented
October, 2005: Another obvious
extension: Modify the program to convert Roman numerals back to
Arabic. (I haven't written this code yet - but I'll bet it's
possible.) |
| Created: September 8, 2000 |
Modified: September 08, 2006
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