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# Conversion of Roman Numbers to Hindu-Arabic

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• 1. Conversion of Roman Numbers to Hindu-Arabic Sualeh Fatehi 1993Although it may seem easy to learn how to form Roman numbers from Hindu-Arabic, and vice versa, theanalysis is quite involved. An analysis of the inter-conversions would lead to the development of amethod or methods of performing these conversions easily. Based on these algorithms, computerprograms could be written to interconvert Roman and Hindu-Arabic numbers, while at the same timechecking that they are not performing the task on incorrectly formed Roman numbers. As the followingdiscussion will show, checking for wrongly formed Roman numbers is more difficult than the actualconversions.Roman numbers are formed differently from Hindu-Arabic numbers, for although based on the radix 10,only two digits are available upto ten videlicet I and V. In addition to this there are other symbols fornumbers ten and greater: X, L, C, D and M, in that order.Therefore, the values of Roman numerals in order are:I 1 V 5X 10 L 50C 100 D 500M 1000Table 1Those on the left may be termed as belonging to the ones group, and those on the right to the fivesgroup.Other numbers are formed by additive or subtractive sequences of these numerals: VI = 6 (additive) andIV = 4 (subtractive). Also, there is no zero, even to be used as a placeholder.This is in contrast to Hindu-Arabic numbers, which have ten digits (being based on 10, and having onedigit for every number up to ten, with zero being used as a placeholder or as a null value). The value ofthe digit depends on its position in the number: 9 followed by two other digits indicates a magnitude of900, but if followed by three digits indicates 9000. Therefore, the Hindu-Arabic system of ciphering is apositional one consisting solely of additive sequences.Because of the positional property of the Hindu-Arabic system, conversion of Hindu-Arabic to Roman isextremely simple, and can be done simply by looking up a table (Table 2) for each digit in a particularposition, and collating the sequence.