lattices and boolean algebra ppt

basic theorems of boolean algebra ppt and laws of boolean algebra ppt
Dr.DouglasPatton Profile Pic
Dr.DouglasPatton,United States,Teacher
Published Date:26-07-2017
Your Website URL(Optional)
Comment
Switching Algebra Fall 2015, Sep 30 . . . www.ThesisScientist.com 1Switching Algebra • A Boolean algebra, where  Set K contains just two elements, 0, 1, also called false, true, or off, on, etc.  Two operations are defined as, + ≡ OR, · ≡ AND. + 0 1 · 0 1 0 0 1 0 0 0 1 1 1 1 0 1 Fall 2015, Sep 30 . . . www.ThesisScientist.com 2Claude E. Shannon (1916-2001) http://www.kugelbahn.ch/sesam_e.htm Fall 2015, Sep 30 . . . www.ThesisScientist.com 3Shannon’s Legacy • A Symbolic Analysis of Relay and Switching Circuits, Master’s Thesis, MIT, 1940. Perhaps the most th influential master’s thesis of the 20 century. • An Algebra for Theoretical Genetics, PhD Thesis, MIT, 1940. • Founded the field of Information Theory. • C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, University of Illinois Press, 1949. A “must read.” Fall 2015, Sep 30 . . . www.ThesisScientist.com 4Switching Devices • Electromechanical relays (1940s) • Vacuum tubes (1950s) • Bipolar transistors (1960 - 1980) • Field effect transistors (1980 - ) • Integrated circuits (1970 - ) • Nanotechnology devices (future) Fall 2015, Sep 30 . . . www.ThesisScientist.com 5Example: Automobile Ignition • Engine turns on when • Ignition key is applied AND • Car is in parking gear OR • Brake pedal is on • AND • Seat belt is fastened OR • Car is in parking gear Fall 2015, Sep 30 . . . www.ThesisScientist.com 6Switching logic Parking gear Seat belt Key Brake pedal Parking gear Motor Battery Fall 2015, Sep 30 . . . www.ThesisScientist.com 7Define Boolean Variables Parking gear Seat belt Key P = 0, 1 S = 0, 1 Brake pedal Parking gear K = 0, 1 M = 0, 1 B = 0,1 P = 0, 1 Motor Battery 0 means switch “off” or “open” 1 means switch “on” or “closed” Fall 2015, Sep 30 . . . www.ThesisScientist.com 8Write Boolean Function Parking gear Seat belt Key P = 0, 1 S = 0, 1 Brake pedal Parking gear K = 0, 1 M = 0, 1 B = 0,1 P = 0, 1 Motor Battery Ignition function: M = K AND (P OR B) AND (S OR P) = K(P + B)(S + P) Fall 2015, Sep 30 . . . www.ThesisScientist.com 9Simplify Boolean Function M = K AND (P OR B) AND (S OR P) = K(P + B)(S + P) = K(P + B)(P + S) Commutativity = K (P + B S) Distributivity Fall 2015, Sep 30 . . . www.ThesisScientist.com 10Construct an Optimum Circuit M = K (P + B S) Parking gear Key P = 0, 1 Brake pedal Seat belt K = 0, 1 M = 0,1 B = 0,1 S = 0, 1 Motor Battery This is a relay circuit. Earlier logic circuits, even computers, were built with relays. Fall 2015, Sep 30 . . . www.ThesisScientist.com 11Implementing with Relays • An electromechanical relay contains: • Electromagnet • Current source • A switch, spring-loaded, normally open or closed • Switch has two states, open (0) or closed (1). • The state of switch is controlled by “not applying” or “applying” current to electromagnet. Fall 2015, Sep 30 . . . www.ThesisScientist.com 12One Switch Controlling Other • Switches X and Y are normally open. • Y cannot close unless a current is applied to X. Y X Y = X Fall 2015, Sep 30 . . . www.ThesisScientist.com 13Inverting Switch • Switch X is normally closed and Y is normally open. • Y cannot open unless a current is applied to X. Y X Y = X Fall 2015, Sep 30 . . . www.ThesisScientist.com 14Boolean Operations • AND – Series connected relays. • OR – Parallel relays. A F F B B A F = A B F = A + B Fall 2015, Sep 30 . . . www.ThesisScientist.com 15Complement (Inversion) A F F A B F = A F = A + B = A · B Fall 2015, Sep 30 . . . www.ThesisScientist.com 16Relay Computers Conrad Zuse (1910-1995) Z1 (1938) Z3 (1941) Fall 2015, Sep 30 . . . www.ThesisScientist.com 17Electronic Switching Devices Electron Tube Point Contact Transistor Fleming, 1904 Bardeen, Brattain, Shockley, 1948 de Forest, 1906 Fall 2015, Sep 30 . . . www.ThesisScientist.com 18Transistor, 1948 The thinker, the tinkerer, the visionary and the transistor John Bardeen, Walter Brattain, William Shockley Nobel Prize, 1956 Fall 2015, Sep 30 . . . www.ThesisScientist.com 19Bell Laboratories, Murray Hill, New Jersey Fall 2015, Sep 30 . . . www.ThesisScientist.com 20

Advise: Why You Wasting Money in Costly SEO Tools, Use World's Best Free SEO Tool Ubersuggest.