boolean-logic - 简化布尔 (X + Y)(X' + Z) = XZ + X'Y

Question

我试图解这个方程，但我得到 z(x + y) + yx'。我也想知道这是否算作交流布尔法则。

标签： boolean-logic

Answer 1

(X + Y)(X' + Z)
XX' + X'Y + XZ + YZ     Distributive law (twice)
F + X'Y + XZ + YZ       Complement law: AA' = F
X'Y + XZ + YZ           Identity law: F + A = A
X'Y + XZ + YZT          Identity law: A = AT
X'Y + XZ + YZ(X + X')   Complement law: T = (A + A')
X'Y + XZ + XYZ + X'YZ   Distributive law
X'Y + X'YZ + XZ + XYZ   Commutative law (twice)
X'YT + X'YZ + XZT + XYZ Identity law (twice): A = AT
X'Y(T + Z) + XZ(T + Y)  Distributive law (twice)
X'YT + XZT              Dominant law (twice): T + A = T
X'Y + XZ                Identity law (twice): AT = A
XZ + X'Y                Commutative law