Quiz 1 Solutions

Mon Sep 18

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

  1. Suppose we have the digits 135, written using base six. What quantity does that represent, expressed in base ten? +4

    The column values in base six are (left to right) 36, 6, and 1. So this number is 1×36 + 3×6 + 5×1 = 36 + 18 + 5 = 59.

  2. Convert the base ten number 178 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 178 only once (so the left digit is 1), and leaves 34 remaining. Twelve divides into 34 just twice, leaving ten remaining. So to represent ten in the ones column, we used the digit ‘X’. Thus the answer is 12X.

  3. Convert the following unsigned binary numbers into base ten. +6

    1. 11100      = 28
    2.   111      =  7
    3. 11010      = 26
    4. 11001      = 25

  4. Convert the following base ten numbers into binary. +6

    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
PDF