To substitute an XOR gate in a circuit, one can use combinations of AND, OR, and NOT gates. The XOR function can be defined in Boolean algebra as XOR = NOT(A) AND B + A AND NOT(B). A truth table for XOR illustrates its output: it returns true (1) when the inputs differ (0,1 or 1,0) and false (0) when they are the same (0,0 or 1,1). For practical implementations, any logic circuit can be constructed using NAND or NOR gates, as these can replicate all other logic functions. If more than two inputs are involved, Karnaugh maps (K-maps) can be utilized to simplify the logic before converting to NAND or NOR forms.