Question: how to construct a table for base 10 for this logic table

https://drive.google.com/file/d/0B2D69u2pweEvaUNnVWdXbm9WT3c/edit?usp=sharing

for base 10

1 op1 5 = 

        01

op1   12

_________

first digit of first number 1     = 1

first digit of second number 1 = 2

 then find 12 in logic table, it is 1, separation is 1 means move the value 1

to left 1 digit become 10

convert 10 back from base 3 to base 10, it is 3

how to construct this unknown name operator table with the custom logic table Min, Except, Diff

based on the operation described

no matter the logic table is correct or not, hope to mechanize these calculation steps for developing 3 operation table for base 10 quickly.

is it possible to develop a new kind of algebra with 3 new operators with the use of 3 operation table?