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Determine whether f is a function from the set of all bit

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 3E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 3E

Determine whether f is a function from the set of all bit strings to the set of integers ifa) f(S) is the position of a 0 bit in S.________________b) f(S) is the number of I bits in S.________________c) f(S) is the smallest integer i such that the ith bit of, S is 1 and f (s) = 0 when S is the empty string, the string with no bits.

Step-by-Step Solution:

Problem 3E

Determine whether f is a function from the set of all bit strings to the set of integers if

a) is the position of a 0 bit in S.

b)  is the number of 1 bit in S.

c)  is the smallest integer i such that the ith bit of, S is 1 and  when S is the empty string, the string with no bits.

                                                                Step by step solution

Step 1 of 3

Part a)  is the position of a 0 bit in S.

The function can exist if there is a 0 bit in S and it does not exist if there are no 0 bits, it is also possible that more than one 0 bits are in S therefore  can have more than one value.

Since, the function definition that it must be unique is not adhered.

Hence, it is not a function.

Step 2 of 3

Chapter 2.3, Problem 3E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Determine whether f is a function from the set of all bit