Addition modulo 2ⁿand XOR addition are two code links which are often used in cipher algorithms, the consistent degree of the two links means the difference degree when the computing sequence is changed in the equation including the two links. The difference function between addition modulo 2ⁿ and XOR addition corresponding to associative law is studied. When the computing sequence of ［(x⊕y)+z］mod 2ⁿ is changed, the computation formulae of the probability distribution of the difference function ξ(x,y,z)=［(x⊕y)+_n^z］⊕［x⊕(y+_n^z)］ is given, and the square sum of the probability is given too. The results presented are useful for some distinguishing attack.