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, $ -&gt; 0$       b, $ -&gt; 1$
a, 0 -&gt; 00       b, 1 -&gt; 11
a, 1 -&gt; \lambda  b, 0 -&gt; \lambda
 

       ------&gt;q1-----------------\lambda, $ -&gt; $------&gt;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.