+ CS 325: CS Hardware and Software Organization and Architecture Gates and Boolean Algebra Part 3

+ Basic Laws of Boolean Algebra Boolean Algebra follows many algebra rules which can be used to make simpler circuits. Example: AB + ACThree gates = A(B + C), Distributive LawTwo gates NameAND FormOR Form Identity Law Null Law Idempotent Law Commutative Law Associative Law Distributive Law Absorption Law De Morgan’s Law

+ Reduction using Boolean Laws

+ Checking Reduction for Correctness

+ Converting Boolean Functions to Standard SOP

+

+ Sum-of-Products

+ ABC

+ Sum-of-Products – Another Example ABC

+ Covered So Far: Logic Gate Diagrams Truth Tables Standard Sum-of-Products Sum of midterms Boolean functions And reduction using Boolean laws You should be able to derive one form using any other form! Truth Table  sum of midterms Reduced Boolean function  standard sum-of-products Logic Gate Diagram  Boolean function  reduced Boolean function  Logic Gate Diagram

+ Product-of-Sums

+ ABC

+ Product-of-Sums - Another Example ABC

+ Covered So Far: Logic Gate Diagrams Truth Tables Standard Sum-of-Products Standard Product-of-Sums Sum of midterms Boolean functions And reduction using Boolean laws

+ Karnaugh Maps Special form of a given truth table. Useful for reducing logic functions into minimal Boolean expressions. B  A ABX

+ Karnaugh Maps 2-Variables Convert the following 2-variable truth table to its Karnaugh map equivalent: B  A ABX

+ Karnaugh Maps 3-Variables The following is an example of a 3-variable truth table converted to its Karnaugh map equivalent: C  AB ABCX

+ Karnaugh Maps 3-Variables Convert the following 3-variable truth table to its Karnaugh map equivalent: C  AB ABCX

+ Karnaugh Maps 4-Variables The following is an example of a 4-variable truth table converted to its Karnaugh map equivalent: CD  AB ABCDX

+ Karnaugh Maps 4-Variables Convert the following 4-variable truth table to its Karnaugh map equivalent: CD  AB ABCDX