Push-down automaton for a language with number of 1s double than 0s
Consider this algorithm:


Initialize a variable $x := 0$.
Scan the string, left to right. If you see $1$, set $x := x + 1$, if you see $0$, set $x := x - 2$.
When you are done, accept iff $x = 0$.


It should be obvious that it recognizes your language. Can you figure out a way to implement it replacing the counter with the stack?