# Quiz 1 Solutions

Wed Jan 31

You have up to 20 minutes. You may use a standard calculator, but no books or notes.

1. Suppose we have the digits 215, written using base six. What quantity does that represent, expressed in base ten?

The column values in base six are (left to right) 36, 6, and 1. So the value 215 represents 2×36 + 1×6 + 5×1 = 72 + 6 + 5 = 83.

2. Convert the base ten number 167 into base twelve. Recall that in base twelve we use the twelve symbols 0,1,2,3,4,5,6,7,8,9,X,E.

The column values in base twelve are (left to right) 144, 12, and 1. (We don’t need a fourth column, which would be 1728.) The third column, 144, divides into 167 only once (so the left digit is 1), and leaves 23 remaining. Twelve divides into 23 just once, leaving eleven remaining. So to represent eleven in the ones column, we used the digit ‘E’. Thus the answer is 11E.

3. Convert the following unsigned binary numbers into base ten.

1. 11100      = 28
2.   111      =  7
3. 11010      = 26
4. 11001      = 25
4. Convert the following base ten numbers into binary.

1. 12      =   1100
2. 17      =  10001
3. 31      =  11111
4. 40      = 101000
5. Convert the following signed numbers into binary using 6-bit signed two’s complement. (Every answer should include all six bits.)

1.  -1      = 111111
2. -17      = 101111
3.  27      = 011011
4. -32      = 100000