### 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.

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

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

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

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

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

- (25 pts) Compute 2
^{12} 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.