add([],[],[]).
add([],Y, Z) :- append([], Y, Z).
add(X,[], Z) :- append(X,[],Z).
 
add([HX|TX],[HY|TY], Z) :-
    HX = 1,
    HY = 1,
    add(TX,TY, Z1),
    add([1],Z1, Z2),
    append([0],Z2,Z),!.
 
add([HX|TX],[HY|TY], Z) :-
    HX = 0,
    HY = 1,
    add(TX,TY,Z1),
    append([1],Z1, Z),!.
 
add([HX|TX],[HY|TY], Z) :-
    HX = 1,
    HY = 0,
    add(TX,TY,Z1),
    append([1],Z1, Z),!.
 
 
add([HX|TX],[HY|TY], Z) :-
    HX = 0,
    HY = 0,
    add(TX,TY,Z1),
    append([0],Z1, Z),!.

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add([1,1,1,1], [1,1],Z).
add([1], [1],Z).
add([1,1,0,1], [1,1],Z).
add([1],[0],Y).
add([0], [1],Z).