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A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable substring containing only 1s. Given a positive integer n, let B(n) be the number of 1-runs in the binary representation of n. For example, B(107) = 3 since 107 in binary is 1101011 which has exactly three 1-runs. What is the following expression equal to? B(1) + B(2) + B(3) + ... + B(255)

A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable substring containing only 1s. Given a positive integer n, let B(n) be the number of 1-runs in the binary representation of n. For example, B(107) = 3 since 107 in binary is 1101011 which has exactly three 1-runs. What is the following expression equal to? B(1) + B(2) + B(3) + ... + B(255)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable substring containing only 1s. Given a positive integer n, let B(n) be the number of 1-runs in the binary representation of n. For example, B(107) = 3 since 107 in binary is 1101011 which has exactly three 1-runs. What is the following expression equal to? B(1) + B(2) + B(3) + ... + B(255)
Transcribed Image Text:A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable substring containing only 1s. Given a positive integer n, let B(n) be the number of 1-runs in the binary representation of n. For example, B(107) = 3 since 107 in binary is 1101011 which has exactly three 1-runs. What is the following expression equal to? B(1) + B(2) + B(3) + ... + B(255)
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