   Chapter 11.4, Problem 20ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# It was shown in the text that the number of binary digits needed to represent a positive integer n is ⌊ log 2 n ⌋ + 1 . Can this also be given as ⌊ log 2 n ⌋ ? Why or why not?

To determine

The number of binary digits needed to represent a positive integer n is log2n+1. Can this also be given as log2n ? Why or why not?

Explanation

Given information:

The number of binary digits needed to represent a positive integer n is log2n+1.

Calculation:

Number of digits in binary notation of n=log2(n)+1

If the number of digits in the binary notation could also be represented by log2(n), then

log2(n)+1=log2(n)

However, this equality is not true for all integers n.

For example, if n = 8:

log2(n)+1=log2(8)

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