automata – Context Free Grammar to Chomsky Normal Form Help

I am trying to convert the following CFG to CNF:

S -> ABS | ε
A -> BSBa | a
B -> Ba | a

The finally result looks like this:

S -> AS’ | AB
S’ -> BS
A -> S’B’ |BB’ | X
B’ -> BX
X -> a
Y -> b
B -> BX | XY

I am fairly new to chomsky normal form, so can anyone verify that I did this right?
Thank you in advance!