Implication and 16 logical operations
72.6K subscribers
SUBSCRIBED
Given two binary inputs p and q, there are four possible assignments of 0's and1's to them, and correspondingly 16 different possible connectives or operations on these four assignments. The systematic study of these 16 connectives forms the foundation for both Boole's algebra, Boolean algebra, and modern circuit analysis. We want to position these subjects so that Boole's algebra is primary. We introduce AND, OR, XOR gate terminology, as well as the negations NOT, NAND, NOR, XNOR and also the implication operations IMP and NIMP. We illustrate the situation with a study of Modus Ponens both through truth tables and a more algebraic analysis based on Boole's algebra. This will give us a powerful new insight that allows us to apply very elementary polynomial algebra to solving complex problems in electrical engineering.