New methods are proposed to implement the exclusive-OR and exclusive-NOR functions at the transistor level under low supply voltage. Since the dynamic power dissipation in CMOS is proportional to Vdd2, low-voltage operation of the circuit is an important issue. The main design objectives for these new circuits are low power dissipation and full-voltage swing at a low supply voltage (Vdd=2 V). The proposed designs are compared with previously known circuits and are shown to provide superior performance. Several XOR circuits have been fully simulated using HSPICE with a 0.4μm CMOS technology at 2 V supply voltage.