IST4_lec12 - IST 4 Information and Logic IST 4 Planned...

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IST 4 Information and Logic
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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
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So Far IST 100 is focusing on CONTEXT… Everything is 0-1 (Two Valued)
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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
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Large Syntax Tables 8 7 6 5 4 3 2 1 0 9 9 7 6 5 4 3 2 1 0 9 8 8 6 5 4 3 2 1 0 9 8 7 7 5 4 3 2 1 0 9 8 7 6 6 4 3 2 1 0 9 8 7 6 5 5 3 2 1 0 9 8 7 6 5 4 4 2 1 0 9 8 7 6 5 4 3 3 1 0 9 8 7 6 5 4 3 2 2 0 9 8 7 6 5 4 3 2 1 1 9 8 7 6 5 4 3 2 1 0 0 9 8 7 6 5 4 3 2 1 0 0 8 7 6 5 4 3 2 1 0 9 1 1 1 1 1 1 1 1 1 1 0 9 1 1 1 1 1 1 1 1 0 0 8 1 1 1 1 1 1 1 0 0 0 7 1 1 1 1 1 1 0 0 0 0 6 1 1 1 1 1 0 0 0 0 0 5 1 1 1 1 0 0 0 0 0 0 4 1 1 1 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1 0 0 1 0 1 0 0 0 2 symbol adder c s d1 d2 c
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Small Syntax Tables 2 symbol adder c s d1 d2 c 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 sum carry
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carry 2 symbol adder c s d1 d2 c sum Syntax Tables to Algebra The Boolean Functions of the Adder
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The Sum Function abc XOR(a,b,c) 000 001 010 011 0 1 1 0 100 101 110 111 1 0 0 1 sum sum
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The Carry Function abc MAJ(a,b,c) 000 001 010 011 0 0 0 1 100 101 110 111 0 1 1 1 carry carry
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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,...
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Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001 Shannon’s advisor both MSc and PhD – a mathematician 70 years
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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
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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
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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 in electrical engineering and one in mathematics Joined MIT in 1936. Passed all requirements for both a master's in electrical engineering and a doctorate in Mathematics, received both degrees in the 1940 commencement
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Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001
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