Convert XOR to NOR - logic

Question

For a course assignment, we were asked to look up how to convert between various logic gates by creating systems involving two inputs A and B and one output O. The last conversion was from XOR to NOR, but I can't seem to find any answers out there. The logic for each of these is as follows:
XOR
A | B | O
----------
0 | 0 | 0
1 | 0 | 1
0 | 1 | 1
1 | 1 | 0
NOR
A | B | O
----------
0 | 0 | 1
1 | 0 | 0
0 | 1 | 0
1 | 1 | 0
For simplicity, I'll request pseudo-code for a function NOR rather than a diagram. The XOR binary operator is ^. The closest I came was the following function in JavaScript:
function nor(a, b) {
return ((a^1)^(a^b))^((b^0)^(a^b));
}
But this is actually the logic for XNOR:
A | B | O
----------
0 | 0 | 1
1 | 0 | 0
0 | 1 | 0
1 | 1 | 1 (this should be 0 though)
Anyone else who can figure this out?
EDIT To summarize, make a NOR operator / function of two arguments using A, B, the constants 0 and 1 as needed, and the only operator allowed is the XOR operator (^).

Answer 1

It is not possible. For instance, you can check
a XOR b XOR 1
to achieve equivalence, but you cannot exclude AND from it, because XOR is not a universal gate.

Answer 2

Not going to give complete solution to homework. But I was curious and so:
You write you have A B and 0 as inputs, but you use a 1 as input in your code.
If you are not allowed to to use 1, you might want to consider what A XOR 0 is.
Your edit looks like 1 is allowed, in which case as far as I can see the solution is to use the direct input in one side of a gate, and a combined input as the other. Like ((a) ^ (a ^ b)).
EDIT Posted the reply without a finished solution so you had something to work on. Just noting it is possible there is no solution.