Quiz 7 - x = 4 5(b(5 points Using the above inverses solve the following algebraic equation in base 5 4 x 3 = 4 subtract 3 from both sides we get 4

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CSE 260-002 QUIZ-8– Sequences and Integer Division: Answer February 29, 2008 20 minutes (30 points) NAME: 1. (5 points) Make the following conversion from base 5 to base 6: 24 5 = x 6 Let’s convert 24 5 to the decimals 24 5 = 2 * 5 + 4 = 14 10 then from decimals to base 6 14 10 14 mod 6: 2, Quotient: 2 2 mod 6: 2 22 6 (5 points) Make the following conversion from base 3 to base 9: 211200221 3 = x 9 9 = 3 2 , so each 2 digits in base 3 correspond to 1 digit in base 9 2 11 20 02 21 3 = 24627 9 2 10 4 10 6 10 2 10 7 10 2. (5 points) Give the following sum using modulo 3 arithmetic. show your carries: 1 1 1 2 1 3 2 2 0 3 -- -- -- 1 1 1 1 3 3. Consider base 5 arithmetic. (a) (5 points) Give the additive inverse for 3 and the multiplicative inverse for 4. additive inverse means 3 + 5 x = 0, so it follows x = 2 5 . multiplicative inverse means 4 * 5 x = 1, so
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Unformatted text preview: x = 4 5 . (b) (5 points) Using the above inverses, solve the following algebraic equation in base 5. 4 x + 3 = 4 subtract 3 from both sides, we get 4 x = 1 from the multiplicative inverse it follows that x = 1 1 4. (5 points) Is the set of all computer programs in a particular programming language countable? Give an intuitive JustiFcation for your answer. It is countable. A program in a particular language can be thought of as a string of bits (each character maps into bits). A string of bits can be mapped into a positive integer. Thus the set of all programs is a subset of N . Since N is countable, set of all computer programs in a particular programming language is countable. 2...
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This note was uploaded on 03/30/2008 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.

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Quiz 7 - x = 4 5(b(5 points Using the above inverses solve the following algebraic equation in base 5 4 x 3 = 4 subtract 3 from both sides we get 4

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