0107-notes

0107-notes - CPSC 121 Lecture 2 January 7 2009 Menu January...

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CPSC 121 Lecture 2 January 7, 2009 Menu January 7, 2009 Topics: Propositional Logic Logic Gates Reading: Today: Epp 1.1, 1.4 January 9: Epp 1.2 Next week:Epp 1.5, 1.3 Handouts: Lab 0 part 1 (repeated) Questionnaire (repeated) Course Outline (on-line only) Reminders: On-line Quiz 2 deadline 9:00pm January 8 On-line/static Quiz 1 (mark has been waived) Labs and tutorials begin week of January 12 www: http://www.ugrad.cs.ubc.ca/~cs121/ WebCT Vista: http://www.vista.ubc.ca The ﬁrst lecture introduced the switch as the fundamental physical structure upon which digital computation is built. The bit (0/1) is the corresponding mathematical abstraction. Switches are concrete. Two things about switches to remember from the ﬁrst lecture: 1) with switches we can compute; and 2) switch technology is an area where it is reasonable to expect both continuous and revolutionary advancement in the years ahead. The six examples included at the end of the last lecture are intended to explore what it means to “prove” something mathematically. Here’s a summary. Spend a moment or two to think about which of the propositions are true, which of them are false and (more importantly as motivation for today) how we might know for sure which are true and which are false. Example Propositions (Summary) Proposition 1: 2 + 3 = 5 Proposition 2: 5 + 3 × 5 = 20 Proposition 3: Intel’s original Pentium processor chip performed ﬂoating point division properly Proposition 4: (Goldbach) Every positive even integer greater than 2 can be written as the sum of two primes Proposition 5: Let n be a natural number. Then the natural number p ( n ) = n 2 + n + 41 is prime Proposition 6: (Euler) There are no positive integers a , b , c , d , such that a 4 + b 4 + c 4 = d 4 Propositional Logic

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Propositional Logic A proposition is a statement that is true or false (but not both) We combine propositions together to create new propositions, called compound propositions
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0107-notes - CPSC 121 Lecture 2 January 7 2009 Menu January...

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