Dual Transformation

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Dual Transformation [Copy link]

The transformation from a logical function to its dual function is called dual transformation. AND and OR, XOR and XOR are two dual operations, the original variable and the inverse variable are dual variables, and " 0 " and " 1 " are dual constants. Operators and variables are always defined in pairs, called dual operators and dual logical quantities, and this special property can be described by dual transformation. 　　The rules of dual transformation are:　　　variables remain unchanged; 　　　constants "0" become "1", "1" becomes "0"; 　　　operators "AND" become "OR", "OR" becomes "AND", "XOR" becomes "XOR", "XOR" becomes "XOR"; 　　　2 or more variables are written without signs. 　　Example: 500)this.style.width=500;"> F









　　　　

　　is the dual function of F , and F and F are each other's dual functions.

　　For a logical algebraic expression expressed as an equation, if both sides of the equation are transformed dually, the equation still holds. This rule is called the duality theorem. The duality theorem is often used to transform logical functions and prove the equality of logical functions. 　　For example:　　　The function of AND-OR form of "XOR" is 500)this.style.width=500;"> ⊙ 500)this.style.width=500;"> 　　Transforming both sides of the above equation dually, we get 500)this.style.width=500;"> This is the function of OR-AND form of "XOR"　　Duality is a basic attribute of logical operations and logical functions, and is also reflected in the structural form of logical circuits. Understanding the duality of logical operations and logical circuits is a basic method to understand logical circuits.