Abstract: Although the output signal of a real XOR gate is spatially related to input signals,in order to simplify the study of optimal low power XOR gate decomposition,present approaches assume that the output signal of a XOR gate is the strict-sense stochastic signal,and directly optimize power dissipation according to probabilities of input signals.In this paper,we not only show the limitations of present approaches through statistics analyses,but also give equations that use transition densities of input signals to compute that of output signal for a real XOR gate.Then,we propose a novel method of optimal low power decomposition for XOR gates.Experiments demonstrate that our approach reduces the power consumption of XOR gates more than three times as present methods do.And the calculated power consumption matches the experimental value with hign accuracy,the error is less than 0.97% on average.