5.11. Convert the proof of Proposition 5.18 into an algorithm and use it to write each of the following numbers n as a sum of positive and negative powers of 2 with at most ½ [log n] + 1 nonzero terms. Compare the number of nonzero terms in the binary expansion of n with the number of nonzero terms in the ternary expansion of n. (a) 349. (b) 9337. (c) 38728. (d) 8379483273489.
5.11. Convert the proof of Proposition 5.18 into an algorithm and use it to write each of the following numbers n as a sum of positive and negative powers of 2 with at most ½ [log n] + 1 nonzero terms. Compare the number of nonzero terms in the binary expansion of n with the number of nonzero terms in the ternary expansion of n. (a) 349. (b) 9337. (c) 38728. (d) 8379483273489.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
(a) only
![Proposition 5.18. Let n be a positive integer and let k = [logn] +1, which
means that 2k > n. Then we can always write
n =
uo+u₁·2+U₂·4+u3 · 8+ ··· + Uk ·
2k
.
with uo, u₁,..., Uk € {−1,0,1} and at most k of the u; nonzero.
(5.5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa332eac-d846-4704-9340-0a50b86bfcea%2F805716d1-bba1-41dd-8150-fa2aeec1a7ae%2Fmxthbfa_processed.png&w=3840&q=75)
Transcribed Image Text:Proposition 5.18. Let n be a positive integer and let k = [logn] +1, which
means that 2k > n. Then we can always write
n =
uo+u₁·2+U₂·4+u3 · 8+ ··· + Uk ·
2k
.
with uo, u₁,..., Uk € {−1,0,1} and at most k of the u; nonzero.
(5.5)
![5.11. Convert the proof of Proposition 5.18 into an algorithm and use it to write
each of the following numbers n as a sum of positive and negative powers of 2 with
at most [logn] + 1 nonzero terms. Compare the number of nonzero terms in the
binary expansion of n with the number of nonzero terms in the ternary expansion
of n.
(a) 349.
(b) 9337. (c) 38728. (d) 8379483273489.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa332eac-d846-4704-9340-0a50b86bfcea%2F805716d1-bba1-41dd-8150-fa2aeec1a7ae%2Fwgm3h_processed.png&w=3840&q=75)
Transcribed Image Text:5.11. Convert the proof of Proposition 5.18 into an algorithm and use it to write
each of the following numbers n as a sum of positive and negative powers of 2 with
at most [logn] + 1 nonzero terms. Compare the number of nonzero terms in the
binary expansion of n with the number of nonzero terms in the ternary expansion
of n.
(a) 349.
(b) 9337. (c) 38728. (d) 8379483273489.
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