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Homework 4 Math for Computer Science Homework

Homework 4 Math for Computer Science Homework

HW 5 Assigned Tuesday 20 March 2018 Due: Tuesday 27 March 2018 1. What are the quotient and remainder when a. 19 is divided by 7? b. −111 is divided by 11? c. 789 is divided by 23? d. 1001 is divided by 13? e. 0 is divided by 19? f. 3 is divided by 5? g. −1 is divided by 3? h. 4 is divided by 1? 2. Suppose that a and b are integers, a ≡ 4(mod13), and b ≡ 9(mod13). Find the integer c with 0≤ c ≤12 such that a. c ≡ 9a(mod13) b. c ≡ 11b(mod13) c. c ≡ a+b(mod13) d. c ≡ 2a+3b(mod13) e. c ≡ a2 +b2 (mod13) 3. Evaluate these quantities. a. 144 mod 7 b. −101 mod 13 c. 199 mod 19 d. 13 mod 3 e. −97 mod 11 HW 5 4. Convert the decimal expansion of each of these integers to a binary expansion. a. 321 b. 1023 c. 100632 5. Convert the binary expansion of each of these integers to a decimal expansion. a. (1 1111)2 b. (10 0000 0001)2 c. (1 0101 0101)2 d. (110 1001 0001 0000)2 6. Convert the octal expansion of each of these integers to a binary expansion. a. (572)8 b. (1604)8 c. (423)8 d. (2417)8 …
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