Kenneth Rosen Edition 7 Exercise 2.3 Question 3 (Page No. 152)

Question

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

1. $f(S)$is the position of a $0$ bit in $S$.
2. $f(S)$is the number of $1$ bits in $S$.
3. $f(S)$is the smallest integer $i$ such that the $i$ th bit of $S$ is $1$ and $f(S)=0$ when $S$ is the empty string, the string with no bits.