You can do it two ways:
(1) you can write functions to convert between LSD and a number of D (for example 13.3.9 would be 13*240+3*12+9=3165), then for the two amounts you want to add, convert them to D, add the D sums together just using normal integer arithmetic and convert the result back, or
(2) you can add individual D values together and handle any overflow into the S calculation, then likewise for S and D, i.e.
D=D1+D2; if D>11 split into D<12 and overflow F;
S=S1+S2+F; if S>19 split into S<20 and overflow F;
I would suggest (1), not because it's easier in the short run, but because sooner or later you are going to need these functions, so you may as well write them in the first instance then you can use them straight away.