## Stony Brook University MAT 118 Spring 2013

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

A. Binary Arithmetic (refer to notes)
1. Convert to binary notation: $47, 80, 1050$.
2. Convert to decimal notation: $110110110, 1010101, 11001100$.
3. Convert to binary and add as binary numbers: $47+80, 47+80+1050$
4. Multiply as binary numbers $10101 \times 10101, 110101 \times 111, 110101101 \times 100000$.
5. Convert to binary numbers and divide. Show quotient and remainder: $25\div 3, 25\div 4, 25\div 5$.
6. 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.