ABSTRACT
It is important to know when two logical statements are equivalent in the context of various applications, whether it be understanding a convoluted statement, specifying a computer search, or designing an efficient computer circuit. We develop certain Rules of Replacement that aid in verifying equivalences; these rules also assist us in carrying out deductive proofs. Replacing the truth-values T and F with the binary numbers 1 and 0, respectively, we can transform compound logical statements into diagrams of digital circuits constructed from certain basic logic gates (and -, or -, not -gates). The Rules of Replacement, together with a graphical representation, can be used to produce efficient and economical designs for digital circuits.
