   Chapter 9.3, Problem 25ES ### 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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# Counting Strings:a. Male a list ol all bil brings ul lengths 0. 1. 2. .V and J dial do not contain the bit pattern 111. b. For each integer n i 0, let </. ™ the number of b« strings of length n dial do not contain die bil pattern HI. Find d+ dt. </></). and dt. C. hind a rccuiicncc relation lot Jlhd,. d2..... d. Use the results of parts < b) and <c) to find the number of bu M ings of length 5 that do not contain die pattern 111.

To determine

(a)

To make a list of all bit strings of lengths 0,1,2,3 and 4 and that don’t contain the bit pattern 111

Explanation

Given information:

Bit strings of binary containing the two bits 0 and 1.

Calculation:

The bit strings of length 0 that don’t contain 111 =0.

The bit strings of length 1 that don’t contain 111 =0,1

To determine

(b)

To find the value of d1, d2

d3 and d4

To determine

(c)

To find the recurrence relation for d1, d2

d3 and d4.

To determine

(d)

To find the number of bit strings of length 5 that do not contain the bit pattern 111.

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