Physics · Ch 9 — Semiconductor Electronics
De Morgan's First Theorem
De Morgan's First Theorem
The first theorem states: the complement of the SUM of two logical inputs equals the PRODUCT of their individual complements, . This is proved by direct truth-table comparison: computing and independently for all four combinations of A and B gives identical output columns in every row, confirming the two expressions are logically equivalent. Since the left side, , is exactly the Boolean equation of a NOR gate, and the right side, , is an AND gate whose TWO INPUTS are each first individually inverted (a so-called 'bubbled AND' gate), the theorem …
What this figure shows. A logic-circuit diagram shows inputs A and B each passed first through their own individual NOT gate (producing and ), and these two inverted signals then feeding into a plain AND gate to give the final output Y -- this 'bubbled AND' arrangement is drawn alongside (or in place of) a single NOR gate symbol to make visually explicit that , i.e. the two cir …