Wed Jan 31

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

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.

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.**Convert the following

**unsigned**binary numbers into base ten.`11100`

=`28`

`111`

=`7`

`11010`

=`26`

`11001`

=`25`

Convert the following base ten numbers into binary.

`12`

=`1100`

`17`

=`10001`

`31`

=`11111`

`40`

=`101000`

Convert the following signed numbers into binary using

**6-bit signed two’s complement.**(Every answer should include all six bits.)`-1`

=`111111`

`-17`

=`101111`

`27`

=`011011`

`-32`

=`100000`