:PROPERTIES: :ID: 54cec9de-d9b0-4c78-8d59-bf75d7ebc133 :mtime: 20231011031213 20231009034736 :ctime: 20231009034715 :END: #+title: Quine-McClusky Method #+filetags: :public:project: * Definition The goal of the QM method is to find the minimised representation of any boolean expression. The QM method is a tabularised method, which is similar to [[id:c3126ca5-44cb-4b50-b8b1-1ce56cc50a6d][Karnaugh Map]]. * Steps of the QM Method 1) make a table, called the QM implication table, to find all the [[id:32c7d004-ec28-4fa7-98d9-d27d653f18f7][Prime Implicant]]. 2) Find the minimum [[id:d7a4c921-b0c1-423c-891a-0fe87ddee4fd][Cover ]]set using the prime implcant chart. * Detailed steps 1) Write down miniterms 2) Group miniterms by number of 1s 3) Compare miniterms that differ by 1 bit 4) Combine the miniterms that differ by 1 bit and replace that bit by "_" 5) put a check mark next to any used miniterms 6) Put the combined terms in the next column 7) Make a QM Prime Implicant Chart 8) Use the QM Prime Implicant Chart to find [[id:7b635cc5-51ae-4c8d-9e18-f8a57a9718b0][Essential Prime Implicant]]. 9) Choose [[id:32c7d004-ec28-4fa7-98d9-d27d653f18f7][Prime Implicant]] to build a [[id:d7a4c921-b0c1-423c-891a-0fe87ddee4fd][Cover]]ing set. * Why does QM Work? If miniterms only differ by 1 bit, they are right next to each other on the [[id:c3126ca5-44cb-4b50-b8b1-1ce56cc50a6d][Karnaugh Map]]. * QM Prime Implicant Chart The QM Prime Implicant Chart plots the unchecked miniterms on the left column and the miniterms (excluding don't care terms) on the top. If there are any columns with a single $X$, that $X$ is an [[id:7b635cc5-51ae-4c8d-9e18-f8a57a9718b0][Essential Prime Implicant]].