MATH130: Quiz 3

Name:
You may use a calculator on this quiz. If you get stuck on a question, move on to the next. If you have time left over at the end of the quiz, check your work. There are questions on both sides of this page.

  1. (10 pts) Convert the base ten number 21 to base two.

     

     

     

  2. (10 pts) Convert the base two number 1101 to base ten.

     

     

     

  3. (10 pts) Put these hexadecimal numbers in order from smallest to largest: 7C, D1, 99, 7A.

     

     

  4. (20 pts) True or false: There exist integers s and t so that 27 = 81 s + 540 t. Briefly explain your answer.

     

     

     

     

     

  5. (25 pts) Find integers a and b for which 6 = 30 a + 42 b.

     

     

     

     

     

     

     

     

  6. (25 pts) Compute 212 mod 17 without using a calculator (show all work).

     

     

     

     

     

     

     

     

     

     

     

     

Bonus: (10 pts) Do there exist integers m and n so that 6 = 18 m + 39 n? Justify your answer.