Brief Introduction to Boolean AlgebraExampleDe’Morgan’s TheoremPowerPoint PresentationSlide 5Brief Introduction to Boolean Algebra•We can use transistors to build AND, OR, NAND, NOR, and Invertors•Manufacturing is simplified with NAND/NOR•NAND/NOR avoid problem with “transistor bleed-through”•Converting between AND/OR circuits and NAND/NOR circuits is easy with Boolean Algebra.•(named for mathematician George Boole)•Boolean Variable: can be in just two states: 0 or 1•Represent Boolean Variables with lettersExample•Two inputs (Boolean variables) A and B are ANDed together.•The AND operation is represented in a Boolean equation with the multiplication symbol (overloading of operator!)•(The OR operation is represented with the addition symbol +)•A AND B can be represented as AB•A OR B can be represented as A + BBADe’Morgan’s Theorem•On of the most useful principles in boolean algebra is De’Morgan’s Theorem, which allows one to switch between ANDs and NORs and OR and NAND•NOT terms or Inverted terms are represented with a line over the terms•AB = A + B •A + B = AB•To convert A+B into a form that can be implemented using a NAND gate follow these steps:•1. Double Complement the term A+B = A+B•2. Use DeMorgan’s to distribute one of the complementsA+B = A BThe equation is now a NAND of the complemented inputs.A B OR A’ B’ A’AND B’ A’NAND B0 0 0 1 1 1 00 1 1 1 0 0 11 0 1 0 1 0 11 1 1 0 0 0 1Note that the third and last columns are equivalent.Complements of input values are easy to get, and may already be