Problem Set: Data Representation

 

  1. Convert the following decimal numbers to 10 bit 2's complement:
    1. 331
    2. -112
    3. 206
  2. Perform the following additions. Assume that all numbers are in 10 bit 2's complement. For each number being added and for the answer, tell whether it is positive or negative. Tell whether there is an overflow.
    1. 1011011100 + 1101100011
    2. 0001011011 + 1101011001
    3. 0101100101 + 0101110100
  3. Perform the following additions. Assume that all numbers are in 32 bit 2's complement. For each number being added and for the answer, tell whether it is positive or negative. Tell whether there is an overflow.
    1. 00 04 02 84 + 39 43 A1 9C
    2. 00 03 5E 99 + FF FA 27 38
    3. FF FD 3A 09 + 00 05 C9 14
  4. Convert the following base 10 numbers to base 2, with at most six places to the right of the binary point:
    1. 147.78125
    2. 91.4483
    3. 232.0897
    4. 29.207
  5. Convert the following base 10 numbers to IEEE single precision floating point. When you count the number of places to compute to the right of the radix point, count the places as you convert from base 10 to base 2, that is, count before you normalize.
    1. 18.125 (compute 6 places to the right of the radix point)
    2. 194.03125 (compute 6 places to the right of the radix point)
    3. -0.23392 (compute 11 places to the right of the radix point)
    4. -3144.56 (compute 10 places to the right of the radix point)
    5. 9,060,100 (estimated population of NJ in 2019)
    6. 0.00031 (compute 16 places to the right of the radix point)
  6. Convert the following IEEE single precision floating point numbers to base 10:
    1. 0011 1110 0100 0000 0000 0000 0000 0000
    2. 1101 0000 0110 0000 0000 0000 0000 0000
    3. 0011 1010 1001 1000 0000 0000 0000 0000
    4. 0011 1101 1010 0110 0000 0000 0000 0000
    5. 1100 0010 1011 0010 1000 0000 0000 0000

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