What just happened

1
01
+01
10

Two D weigh the same as one C, so you could take the two D off and put one C on instead.

In the D column, 1 + 1 is two D. That is one C and no D: write 0 under D and carry 1 into the C column.

Putting one thing in place of something equal to it is called substitution.

Moving the extra into the next column is called carrying.

OK