<P> An XOR gate circuit can be made from four NAND gates . In fact , both NAND and NOR gates are so - called `` universal gates '' and any logical function can be constructed from either NAND logic or NOR logic alone . If the four NAND gates are replaced by NOR gates , this results in an XNOR gate , which can be converted to an XOR gate by inverting the output or one of the inputs ( e.g. with a fifth NOR gate ) . An alternative arrangement is of five NOR gates in a topology that emphasizes the construction of the function from ( A + B ) ⋅ ( \ displaystyle ( A + B ) \ cdot ) ( A  ̄ + B  ̄ ) ( \ displaystyle ( ( \ overline ( A ) ) + ( \ overline ( B ) ) ) ) ( noting from de Morgan 's Law that a NOR gate is , in effect , an inverted - input AND gate ) . Two possible configurations constructed from NAND gates and two possible configurations constructed from NOR gates are shown below . </P>
<P> An XOR gate circuit can be made from four NAND gates . In fact , both NAND and NOR gates are so - called `` universal gates '' and any logical function can be constructed from either NAND logic or NOR logic alone . If the four NAND gates are replaced by NOR gates , this results in an XNOR gate , which can be converted to an XOR gate by inverting the output or one of the inputs ( e.g. with a fifth NOR gate ) . An alternative arrangement is of five NOR gates in a topology that emphasizes the construction of the function from ( A + B ) ⋅ ( \ displaystyle ( A + B ) \ cdot ) ( A ̄ + B ̄ ) ( \ displaystyle ( ( \ overline ( A ) ) + ( \ overline ( B ) ) ) ) ( noting from de Morgan 's Law that a NOR gate is , in effect , an inverted - input AND gate ) . Two possible configurations constructed from NAND gates and two possible configurations constructed from NOR gates are shown below . </P>
xor gate using minimum number of nand gates
xor gate using minimum number of nand gates
four
four