# PDA of the language where the number of a's are NOT equal to the number of b's

I have this NPDA for language L = {w: num_a(w) == num_b(w)}
all loops in q1  a, $$-> 0$$ b, $$-> 1$$ a, 0 -> 00 b, 1 -> 11 a, 1 -> \lambda b, 0 -> \lambda   ------>q1-----------------\lambda, $$->$$------>q2  initial state: q1
final state: q2
What if I modified L such that the number of a's is not equal to number of b's.
That is L' = {w: num_a(w) != num_b(w)}. What would be the modification I have to make in the original NPDA.

Your PDA can act as follows. For each $$a$$ being read, it pushes $$A$$ into the stack. Then, for every $$b$$ being read, it attempts to pop $$A$$ off the stack. If there are no more $$A$$s, it moves to an accepting state, checking that the rest of the input consists of $$b$$s; this handles the case in which there are more $$b$$s than $$a$$s. Alternatively, it could decide at some point to move, via an $$\epsilon$$ transition that pops an $$A$$, to a different accepting state at which no more symbols can be read; this handles the case in which there are more $$a$$s than $$b$$s.