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IST4_lec3

# IST4_lec3 - 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
HW #1 Due Tuesday, 4/15 MQ1 People with an Unusual Memory Due Thursday, 4/10 Please email PDF (not doc) After hours building access (TA hours): should work?!?

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What is the number? What is the number? 31 31x60 31 + = 1891 Babylonian Number Systems

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The Babylonians knew everything!

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So Far. ..
< Composition Comparing two quantities - which one is bigger? Domination principle: find the most significant position the numbers differ? 79123456780 71234567890 ?

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Domination Principle Domination principle for weighted representations: When representing a number, use a new (larger) weight only when you reach the maximum value you can use with smaller weights new weight maximal value using smaller weights A given weight can be used only up to a limit (base)
Domination Principle – Base 10 new weight 10 99 100 999 1000 9 maximal value using smaller weights

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Domination Principle – Base b Proposition: for any b>1, Proof: maximal value using smaller weights new weight Q
ist A ‘mysterious’ number representation system?? ?? What is the base 10 representation? Factoradic Number System

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< Does the domination principle hold in the Factoradic number system? 100000 54321 vs Domination Principle – Factoradic Domination Principle YES
Domination Principle – Factoradic Proposition: for any p>0, Proof: new weight Q by induction maximal value using smaller weights base case is easy: p=2, (1+4 = 6-1) need to prove: ??

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Counting Sheep
Suppose that he has only 3 different sticks, how will you record the number?

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IST4_lec3 - IST 4 Information and Logic IST 4 Planned...

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