IST4_lec3

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

Info iconThis preview shows pages 1–20. Sign up to view the full content.

View Full Document Right Arrow Icon
IST 4 Information and Logic
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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?!?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
What is the number? What is the number? 31 31x60 31 + = 1891 Babylonian Number Systems
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
The Babylonians knew everything!
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
So Far. ..
Background image of page 8
< Composition Comparing two quantities - which one is bigger? Domination principle: find the most significant position the numbers differ? 79123456780 71234567890 ?
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 10
Domination Principle – Base 10 new weight 10 99 100 999 1000 9 maximal value using smaller weights
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Domination Principle – Base b Proposition: for any b>1, Proof: maximal value using smaller weights new weight Q
Background image of page 12
ist A ‘mysterious’ number representation system?? ?? What is the base 10 representation? Factoradic Number System
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Factoradic number system: Factoradic Number System
Background image of page 14
Factoradic Number System
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
< Does the domination principle hold in the Factoradic number system? 100000 54321 vs Domination Principle – Factoradic Domination Principle YES
Background image of page 16
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: ??
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Counting Sheep
Background image of page 18
Suppose that he has only 3 different sticks, how will you record the number?
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 20
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 50

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

This preview shows document pages 1 - 20. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online