Physics · Ch 9 — Semiconductor Electronics
De Morgan's Second Theorem
De Morgan's Second Theorem
The second theorem states: the complement of the PRODUCT of two logical inputs equals the SUM of their individual complements, . Just as with the first theorem, 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. Since the left side, , is exactly the Boolean equation of a NAND gate, and the right side, , is an OR gate whose TWO INPUTS are each first individually inverted (a 'bubbled OR' gate), the theorem also says a NAND gate is functionally identical to a bubbled OR gate. …
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 OR gate to give the final output Y -- this 'bubbled OR' arrangement is drawn alongside (or in place of) a single NAND gate symbol to make visually explicit that , i.e. the two cir …