Chapter $1$ Exercises:

Modify the decimal addition algorithm of Figure $1\mathrm{.}2$ so that the two numbers being added need

not have the same number of digits. That is$,$ the algorithm should be able to add a value a containing

$m$ digits to a value $b$ containing $n$ digits, where $m$ may or may not be equal to $n.$

The following is Euclid's $2,300-$year$-$old algorithm for finding the greatest common divisor of

two positive integers I and J$.$

a$.$ Go through this algorithm using the input values $20$ and $32.$ After each step of the algorithm

is completed, give the values of I, J$,$ and R$.$ Determine the final output of the algorithm.

b$.$ Does the algorithm work correctly when the two inputs are $0$ and $32?$ Describe exactly what

happens, and modify the algorithm so that it gives an appropriate error message.