Question $3$

$12\mathrm{.}5pts$

When we described the checksum system for binary messages in class, we added the number of $1\text{'}$s in the ASCII representation of the message and tacked on the binary representation of the sum to the end. In our example, the checksum was encoded by $8$ bits. For this problem, let's suppose that we are going to represent the checksum with $9$ bits instead.

Of course, representing the sum of a long message might require more than $9$ bits. As such, we won't tack on the total sum of all of the $1\text{'}$s$,$ but instead the sum $($ modN. What is the most sensible choice for $N?$

$9$

$81$

$256$

$512$

$1024$