IST4_lec4

IST4_lec4 - IST 4 Information and Logic IST 4 Planned...

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IST 4 Information and Logic
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mon tue wed thr fri 31 M1 1 7 M1 14 2 1 21 3 2 28 3 5 4 12 5 4 19 26 6 5 2 6 IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T T Mx= MQx out Mx= MQx due midterms midterms
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HW #1 Due Tuesday, 4/15 at 2:30pm in class MQ1 People with an Unusual Memory Due today by 10pm - 4/10 Please email PDF to [email protected]
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So Far. ..
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So Far. .. The Babylonians knew everything! It is all about SYNTAX. ..
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The Factoradic number system: Factoradic Number System
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Counting Sheep with seven sticks can count up to 7! = 5040 2 4 3 2 2 0 0 1 0 1 3 0 1 2 4 0 1 3 5 1 0 2 5 4 3 6 0 1 copy if smaller increase by 1 if bigger or equal decimal <-> factoradic <-> permutations in lexicographoc
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An Optimally Balanced Construction for Flash Memories 1234 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 3 2 1 4 2 3 4 1 3 4 1 2 4 1 2 3 1 2 3 4 1 3 4 2 4 2 1 3 3 4 2 1 2 1 3 4 3 2 4 1 4 1 3 2 2 4 1 3 1 3 2 4 4 3 1 2 1 2 4 3 2 4 3 1 3 1 2 4 4 3 2 1 1 4 3 2 2 1 4 3 3 2 1 4 4 2 3 1 3 1 4 2 1 4 2 3 2 3 1 4
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Balanced Order Permutation for Flash Memories 2 3 4 1 3 4 1 2 4 1 2 3 1 2 3 4 1 3 4 2 4 2 1 3 3 4 2 1 2 1 3 4 3 2 4 1 4 1 3 2 2 4 1 3 1 3 2 4 4 3 1 2 1 2 4 3 2 4 3 1 3 1 2 4 4 3 2 1 1 4 3 2 2 1 4 3 3 2 1 4 4 2 3 1 3 1 4 2 1 4 2 3 2 3 1 4 Question: Is there a simple mapping between the decimals and balanced order permutations ?
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Yes! due to Robert Mateescu decimal permutation lexicographic order factoradic decimal permutation balanced order b-factoradic? Question: Is there a simple mapping between the decimals and balanced order permutations? Balanced Order Permutation for Flash Memories
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The factoradic number system for n=4: B-Factoradic Number System 6 2 1 {0-3} {0-2} {0-1} 221 2 x6 + 2 x2 + 1 x1 = 17 The b-factoradic number system for n=4: 11 1 1 x12 + 1 x4 + 1 x1 = 17 12 4 1 {0-1} {0-2} {0-3} 2 3 4 24 24 2 3 4 Does the domination principle hold for b-factoradic? 22= 3 x6+ 2 x2 + 0 x1 22= 1 x12 + 2 x4 + 2 x1
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Back to Composition Combining two quantities – adding two numbers? 2008 + 1891 = 3899
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Addition with Roman Numerals MMVIII 2008 MDCCCLXXXXI + IIII XXXX V L CCC D MMM 3899 aggregating identical symbols, is it enough?
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VIIII 9 MDCCCCLXXXXI + IIIII XXXX V L CCCC D M 1991 V XXXX V L CCCC D M XXXX X L CCCC D M L L CCCC D M C CCCC D M D D M MM 2000 Addition with Roman Numerals aggregating identical symbols, is it enough? no, need compression!
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Addition with Roman Numerals It’s all About Syntax IIIII XXXXX V LL CCCCC DD MMMMM C M VV X L D V 5 blue symbols transform to the next yellow symbol 2 yellow symbols transform to the next blue symbol compression rules
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Addition with Roman Numerals It’s all About Syntax 5 blue symbols transform to the next yellow symbol 2 yellow symbols transform to the next blue symbol Shannon 1916-2001
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The Abacus: It’s all About Syntax I V X L C D V M LL DD C M VV X IIIII XXXXX V CCCCC MMMMM L D V
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I V X L C D V M LL DD C M VV X IIIII XXXXX V CCCCC MMMMM L D V The Abacus: It’s all About Syntax What is the number?
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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_lec4 - IST 4 Information and Logic IST 4 Planned...

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