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# s1 - Selected Solutions to Homework 1 Please post questions...

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Selected Solutions to Homework # 1 Please post questions to the discussion forum or stop by during office hours if you have questions about the first or third problem (truth tables and the problem about quotients and remainders using your calculator). # 2: Here is a solution to part (b) ii: Divide a by b where a = 2011 and b = 13 represent numbers written in base 7. This means that a = (2011) 7 and b = (13) 7 . There are two approaches. The first approach is to convert to base 10, divide as usual, and then convert the answers back to base 7. Convert to base 10: a = (2011) 7 = 2 * 7 3 + 0 * 7 2 + 1 * 7 1 + 1 * 7 0 = 2 * 343 + 0 + 7 + 1 = 694 b = (13) 7 = 7 + 3 = 10 Divide: 694 = 69 * 10 + 4 Convert back to base 7: (2011) 7 = (126) 7 * (13) 7 + (4) 7 (To obtain the base 7 representation of 69, you can successively divide by 7: 69 = 9 * 7 + 6 , 9 = 1 * 7 + 2 , 1 = 0 * 7 + 1 The remainders are 6 = r 0 , 2 = r 1 , and 1 = r 2 , where the notation r i follows the fourth problem on the homework.) The second approach is to perform long division in base 7. (For sim- plicity of notation, I will supress the base seven subscript.) We see that 13 goes into 20 once...

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s1 - Selected Solutions to Homework 1 Please post questions...

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