Quiz 1 Answer Key
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1) Find the value of x if (113) base x = (11110011) base 2

   11110011 = (243) base 10

   x^2 + x + 3 = 243
   x^2 + x - 240 = 0
   (x + 16)(x - 15) = 0
   
   x = 15

2) Give the IEEE754, single precision representation of 20.

   There is 1 sign bit, 8 exponent bits, 23 magnitude bits in IEEE754 
   representation. 

   IEE754 assumes a hidden 1.  Exponent is in Excess-127 format.
   
   20 = 1.25 * 2^4

   So, the exponent is 4 + 127 = 131 = 1000 0011
       the magnitude is 0.25   = 010 0000 0000 0000 0000 0000
       the sign is positive    = 0

   The binary representation, thus, is:

      0100 0001 1010 0000 0000 0000 0000 0000


3) The 7321 representation for the ten decimal digits, 0 through 9, are:

      7  3  2  1

    0  0  0  0  0
    1  0  0  0  1
    2  0  0  1  0
    3  0  1  0  0   OR  0  0  1  1 
    4  0  1  0  1
    5  0  1  1  0
    6  0  1  1  1
    7  1  0  0  0
    8  1  0  0  1
    9  1  0  1  0

    So the answer for Part 1:
      6 = 0111
      9 = 1010

    The answer for Part 2:
      3 can be representated by either 0100 or 0011