## Stony Brook University

MAT 118 Spring 2013

### Assignment 8 due in Recitation, week of April 1

A. Binary Arithmetic (refer to notes)
- Convert to binary notation: $47, 80, 1050$.
- Convert to decimal notation: $110110110, 1010101, 11001100$.
- Convert to binary and add as binary numbers: $47+80, 47+80+1050$
- Multiply as binary numbers $10101 \times 10101, 110101 \times 111,
110101101 \times 100000$.
- Convert to binary numbers and divide. Show quotient and
remainder: $25\div 3, 25\div 4, 25\div 5$.
- Divide as binary numbers. Show quotient and
remainder: $10111011\div 100, 10111011\div 101$.

B. Prime numbers. We worked the Sieve of Eratosthenes in class
for numbers up to $100$. (This is also worked out in the text).
Work the sieve by hand for numbers from $1$ to $200$. Note that since
$15^2 > 200$, you only need to cancel multiples of primes
up to $13$, i.e. $2, 3, 5, 7, 11, 13$. Circle the prime
numbers you have found.

C. Search the internet for news of the largest prime number
known (one was discovered very recently). Report what you have
found.

Remember: Collaboration is fine, but
what you hand in *should be your own work.* Handing in
something you copied is plagiarism and will cost you if it is
detected. Write down what you tried and how it worked.