IST4_lec13

IST4_lec13 - 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 Please send a pdf file named yourname-mq2.pdf to ta4@paradise.caltech.edu
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Some Major Mile stones in the Development of Information ‘Universal Language/Syntax Dream’ calculus, binary systems, logic. .. ‘Algebra to Physics’ automatic syntax processing with relay circuits, information Theory. ... ‘The Babylonian Knew Everything’ masters of syntax , base-60 positional system, abacus,. .. ‘Logic to Algebra’ Boolean algebra for syntax processing. ..
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Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001 Posted on the class web site HW #5 (this Thursday) is focusing on relay circuits
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Boolean Calculus and Physical Circuits Single Lines and Composition The language of lines: A line can have only two possible colors: blue or red Two lines can be composed in two possible ways In parallel: In series:
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Boolean Calculus and Physical Circuits Endpoints Compositions of lines have endpoints In parallel: In series: Lines have endpoints
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Boolean Calculus and Physical Circuits Composition Compositions of lines can be composed in two different ways, using their endpoints In parallel: Compositions can be treated as if they are lines Lines have endpoints a b a b
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Boolean Calculus and Physical Circuits Composition Compositions of lines can be composed In two different ways, using their endpoints In series: Compositions can be treated as if they are lines Lines have endpoints a b a b
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Boolean Calculus and Physical Circuits Color of Composition What is the color of a composition? Compositions can be treated as if they are lines color = blue color = red The color of a composition is red if there is a red path between the endpoints Otherwise, the color is blue
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Algebraic system : set of elements B, two binary operations + and B has at least two elements (0 and 1) Two-Colored Line Composition is a 0-1 Boolean Algebra Elements: 0 1 Operations: + Compose in series: Compose in parallel: + The color of a composition is red if there is a red path between the endpoints. Otherwise, the color is blue
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In parallel: In series: + Two-Colored Line Composition is a 0-1 Boolean Algebra
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Boolean Algebra : set of elements B={0,1}, two binary operations OR and AND xy OR(x,y) 00 01 10 11 0 1 1 1 xy AND(x,y) 00 01 10 11 0 0 0 1 0 iff both x and y are 0 1 iff both x and y are 1 + The color of a composition is red if there is a red path between the endpoints. Otherwise, the color is blue Two-Colored Line Composition is a 0-1 Boolean Algebra
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Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001 1 Relay on the edge controlled by a 0-1 variable 0 0 1
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Connection Between Boolean Calculus and Physical Circuits Shannon 1938 Shannon 1916-2001 0 The value of a circuit is 1 if there is a connected path between the endpoints Otherwise, it is 0 0 1 1 The color of a composition is red if there is a red path between the endpoints Otherwise, the color is blue
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IST4_lec13 - IST 4 Information and Logic IST 4: Planned...

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