### Daniel's Ethiopic Number Algorithm #4

For one reason or another during the last four years it seems necessary that each year I write a new number algorithm for converting Arabic numbers into Ethiopic. Usually this happens as a memory test that fails and then a new algorithm is created and new insight gained. This year I was finally getting around to HTMLing last year's algorithm but couldn't find it! I tried to rediscover it from some computer code but ended up inventing yet another algorithm.

I think this one is pretty simple, I've tried to emphasize that in the presentation below. The key is that numbers are read in groups of 2 and each group gets the same conversion process. There is only a single special rule that is discussed at the end:

 1) 7,654,321 Start with an arbitrary number. 2)     From left to right group numbers in sets of 2. 3) 3 2 1 0 We'll add subscripts for book keeping. 4) 3 [60+5]2 [40+3]1 [20+1]0 Now expand the sets into 10's and 1's. 5) ()3 ()2 ()1 ()0 Write expansions as seperate numbers. 6) ( )3 (  )2 (  )1 (  )0 Go ahead and convert to Ethiopic numbers. 7) ( ) + (3 * { }) (  ) + (2 * { }) (  ) + (1 * { }) (  ) + (0 * { }) The subscripts now tell how many 's we need. 8) ( ) + ( + + ) (  ) + ( + ) (  ) + ( ) (  ) + (0) 9) ( ) + ( + ) (  ) + ( ) (  ) + ( ) (  ) + (0) Reduce as per = + 10)           Group... 11)           Collect and we're done! Note! Except for when we use subscript ``0'' (the far right side) there is a rule that 1's in the 1's place are absorbed by an , , or on the right. So if we changed the ``5'' in 2 to a ``1'' in the above; the reduction would go: as 3) 3 2 1 0 We'll add subscripts for book keeping. : : : : : : 9) ( ) + ( + ) (  ) + ( ) (  ) + ( ) (  ) + (0) Reduce as per = + 10)          Group...

The interesting consequence then is that can only appear in the one's place (the far right)!