NOR gates are actually commonly used, as are AOIs/OAIs in many technologies (and or inverters, 3-input circuits that are common in adders). OR and AND cannot b

NOR gates are actually commonly used, as are AOIs/OAIs in many technologies (and or inverters, 3-input circuits that are common in adders). OR and AND cannot be built directly in CMOS technology. The most efficient way to build them is by combining a NOR/NAND with an inverter. Edit: To clarify, I believe there are cell libraries that do have OR and AND, but the transistor count is the same as NOR/NAND + inverter, so it's a bit questionable whether there's really an advantage to using them.