CSC 311 Practice Problem Set #1

  1. Assuming two's complement, give the result of 00000000 - 11111111. Also indicate the result in decimal.
  2. Assuming two's complement, give the result of 11001011 + 11110010. Also indicate the result in decimal.
  3. Write a Boolean expression that represents this circuit.
  4. Write a truth table that represents the circuit above.
  5. Draw a circuit equivalent to the boolean expression ((A + B)' (BC)')'
  6. Prove xy + xy' = x using truth tables.
  7. Show that (A + B)' (A' + B')' = 0.
  8. Show how the AND function can be constructed from two NAND gates.
  9. Which of the following are valid hexadecimal numbers? BED, CAB, DEAD, DECADE, ACCEDED, BAG.
  10. Assuming no sign bit, give the result of 2A31BD6F + 33333333.
  11. Most people can only count to 10 on their fingers; however, computer scientists can do better. If you regard each finger as one binary bit, with finger extended as 1 and finger touching palm as 0, how high can you count using both hands?
  12. Describe a simple way we could multiply 00001010 and 00000011 without doing any conversions to decimal.

Answers to these questions are available here.

Below are some more practice problems for drawing circuit diagrams and number conversions. There will be no answers provided for these.

  1. F = A xor (BD)
  2. F = (B + C)(A + D)'(E + F)
  3. F = ( (AB)' + C')'  (Note: on this one, try to use the minimum # of gates)
  4. F = (A' + B + C) xor (ABC)'
  5. Convert to hex: 0011100011100101
  6. Convert to hex: 101.125
  7. Convert to decimal: 2A3.4
  8. Convert to binary: 16BD001CA.5F
  9. Convert to binary: 99.6031
  10. Convert the previous two answers into IEEE single precision format
  11. Convert into IEEE single precision: -205.771