How do I make a logic gate that takes 4 input and gives and output if only one is powered?
Being X is your output, and A, B, C and D are your inputs,
X = ((A && !B && !C && !D) || (!A && B && !C && !D) || (!A && !B && C && !D) || (!A && !B && !C && D))
There are better methods, but this is one of the simplest to derive. && is an AND gate, and || is an OR gate.
The brackets group simultaneous lines/operations.