IST4_lec12

IST4_lec12 - IST 4 Information and Logic 1 M1 31 6 2 6 5 26...

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Unformatted text preview: IST 4 Information and Logic 1 M1 31 6 2 6 5 26 19 M2 5 4 12 4 5 3 M2 28 3 2 21 2 1 14 M1 7 fri thr wed tue mon IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T Mx= MQx out Mx= MQx due T Old/Odd Machines that Compute So Far IST 100 is focusing on CONTEXT… Everything is 0-1 (Two Valued) Algorithms – Syntax Manipulation syntax for number systems How is it related to Boolean algebra? Boolean algebra is a formal system for syntax manipulation Today: How is the algebra related to circuits? A relay circuit is a physical system for syntax manipulation Large Syntax Tables 8 7 6 5 4 3 2 1 9 9 7 6 5 4 3 2 1 9 8 8 6 5 4 3 2 1 9 8 7 7 5 4 3 2 1 9 8 7 6 6 4 3 2 1 9 8 7 6 5 5 3 2 1 9 8 7 6 5 4 4 2 1 9 8 7 6 5 4 3 3 1 9 8 7 6 5 4 3 2 2 9 8 7 6 5 4 3 2 1 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 9 1 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 7 1 1 1 1 1 1 6 1 1 1 1 1 5 1 1 1 1 4 1 1 1 3 1 1 2 1 1 9 8 7 6 5 4 3 2 1 1 1 2 symbol adder c s d1 d2 c Small Syntax Tables 2 symbol adder c s d1 d2 c 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 sum carry carry 2 symbol adder c s d1 d2 c sum Syntax Tables to Algebra The Boolean Functions of the Adder The Sum Function abc XOR(a,b,c) 000 001 010 011 1 1 100 101 110 111 1 1 sum sum The Carry Function abc MAJ(a,b,c) 000 001 010 011 1 100 101 110 111 1 1 1 carry carry Evolution of Computing syntax for number systems (algorithms) Boolean algebra is a formal system for syntax manipulation A relay circuit is a physical system for implementing Boolean functions Binary syntax for number systems Beginning: computing (manually/mechanically) with physics (notches, abacus) Modern computing: automatic manipulation of syntax electrical (physics), chemical, biological,... Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001 Shannon’s advisor both MSc and PhD – a mathematician 70 years Shannon’s Inspiration Joined MIT in 1936 Shannon 1916-2001 The differential analyzer at MIT (1931) was the first general equation solver It could handle sixth-order differential equations Vannevar Bush 1890 – 1974 Samuel Caldwell 1904-1960 Shannon’s Background Shannon 1916-2001 Claude Elwood Shannon was born in Petoskey, Michigan, on April 30, 1916 . The first sixteen years of Shannon's life were spent in Gaylord, Michigan His father, Claude Sr. (1862-1934), a descendant of early New Jersey settlers, was a businessman and for a period a Judge of Probate His mother, Mabel Wolf Shannon (1880-1945), daughter of German immigrants, was a language teacher and for a number of years Principal of Gaylord High School, in Gaylord, Michigan Shannon’s Background Shannon 1916-2001 Claude Elwood Shannon was born in Petoskey, Michigan, on April 30, 1916 . The first sixteen years of Shannon's life were spent in Gaylord, Michigan In 1932 he entered the University of Michigan, where he took a course that introduced him to the work of George Boole He graduated in 1936 with two bachelor's degrees, one...
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This note was uploaded on 12/12/2009 for the course IST 4 taught by Professor Shuki during the Spring '09 term at Caltech.

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IST4_lec12 - IST 4 Information and Logic 1 M1 31 6 2 6 5 26...

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