Python 3 - 50 bytes
r=str.replace r(r(r(input(),'1','a'),'0','1'),'a','0') It's not as short as some of the other ones, but it takes a different approach.
daviewales
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r=str.replace r(r(r(input(),'1','a'),'0','1'),'a','0') It's not as short as some of the other ones, but it takes a different approach.