If $G'(s)=G(s0^{|s|})$ and $G$ is a PRNG, is $G'$ necessarily a PRNG?
Suppose g is a PRNG. $\:$ Define G by the following pseudocode:

def G(w):
 m = length(w)
 n = ceiling(m/2)
 set x equal to the n leftmost bits of w
 set y equal to the m-n rightmost bits of w
 z = concatenate(g(x),y)
 output z


In this case, G is a PRNG and G' is not a PRNG.