Polynomial expressions of the form an3 bn2 cn d can be

Chapter 9, Problem 9.3.19

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Polynomial expressions of the form an3 bn2 cn d can be used to express positive integers, such as 4573, using different powers of 10: 4573 5 4?1000 1 5?100 1 7?10 1 3 or 4573 5 4?103 1 5?102 1 7?101 1 3?100 or if n 5 10, 4573 5 4?n3 1 5?n2 1 7?n1 1 3?n0 5 4n3 1 5n2 1 7n 1 3 Notice that in order to represent any positive number, the coefficient multiplying each power of 10 must be an integer between 0 and 9. a. Express 8701 as a polynomial in n assuming n 10. b. Express 239 as a polynomial in n assuming n 10. Computers use a similar polynomial system, using binary numbers, to represent numbers as sums of powers of 2. The number 2 is used because each minuscule switch in a computer can have one of two states, on or off; the symbol 0 signifies off, and the symbol 1 signifies on. Each binary number is built up from a row of switch states, each set at 0 or 1 as multipliers for different powers of 2. For instance, in the binary number system 13 is represented as 1 1 0 1, which stands for 1?23 1 1?22 1 0?21 1 1?20 5 1?8 1 1?4 1 0?2 1 1?1 5 8 1 4 1 1 5 13 c. What number does the binary notation 1 1 0 0 1 represent? d. Find a way to write 35 as the sum of powers of 2; then give the binary notation.

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