Math 113 Multiplying Roman Numerals

It's not as ugly as I thought. Multiplying numbers that are represented as Roman numerals is notas bad as it would seem For example, let's multiply 127 by 34.

127 The usual decimal method: x 35 635 Before doing this with Roman numerals, we'll first show the method 381_ using decimal notation.4445

127 35 The first column is gotten by doubling the preceding number; 254 17 the second column is done by halving the preceding number (toss any remainders) 508 81016 4 Then the underlined values are added - these correspond to the odd numbers in2032 2 column 2.4064 1

127 This method is really like writing the second number in binary notation: 254 35 = 1 + 2 + 32 = 1·1 + 1·2 + 0·4 + 0·8 + 0·16 + 1·32 The 1's correspond with4064 the odd numbers in column 2 and the zeros with the even numbers.4445

This second method is pretty efficient and works pretty well with Roman numerals.

C XX VII XXXV odd C XX VII(CC XXXX XIIII) CC L IIIICC L IV XVII odd + MMMM LX IIII(CCCC C VIII) MMMM CCC C XXX VVV = MMMM CD XL VD VIII VIIIM X VI IVMM XX X II IIMMMM LX IV 1 odd

Here's another example:

MMXVI LI odd MM X VIMMMM XX XII XXV odd MMMM XX XIIV MMM LX IV X II XXX MM CC L VI X V M C XX VIII VI LX MMMM D XIIXXX MM CC L VI III odd C MM DCC C X VI

LX M MMM D XII I odd

The numerals with bars on the top are worth 1000 times the given value. So the answer to this problem is 102,816 in decimal notation.