Summer A 2001, Assignment 1

Due 5/17 at the start of class.

  1. (2 points) Draw circuits for the following and prove whether or not they are equivalent by using truth tables. Do not simplify the expressions. (! is NOT).
  2. (2 points) Draw a 2-to-4 decoder circuit using only 2-input NOR gates. You may use as many of them as needed. You may ONLY use NOR gates to implement the entire circuit.
  3. (4 points) Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 0, 3, 5, 6.
  4. (2 points) Consider the three input boolean function that is 1 if the binary equivalent of the inputs is 1, 2, or 7. Draw a circuit diagram for this function using the MSI multiplexer chip on  page 132. Label the input lines as D, E, and F instead of A, B, and C.
  5. (3 points) Redo the previous two questions, but implement both circuits on the same LSI PLA. Label the inputs for each differently (eg: A, B, C for question 3 and D, E, F for question 4). Draw all the lines that you use into each AND gate (12 for each AND gate). Draw all the output lines from the AND gates that you use into each of the OR gates you use. Indicate which fuses have been blown, and which have not.
  6. (4 points total) A 2-bit demultiplexer is a circuit whose single input line is steered to one of the four output lines depending on the state of the two control lines.
    1. (1) Draw the truth table for a 2-bit demultiplexer. There will be one input variable, two control variables, and 4 output variables.
    2. (2) Draw the circuit for a 2-bit demultiplexer.
    3. (1) Draw the circuit for a 3-bit demultiplexer. There will be one input line, three control lines, and 8 output lines.
  7. (3 points) Using the MSI Multiplexer chip on page132, implement the 4-input boolean function that is a 1 when the binary equivalent of the inputs is 1, 7, 9, 10, 12, or 15 . Label the 4 inputs as A, B, C, and D. You may use an additional inverter. You must use the multiplexer as it is shown: it has only three input lines, A, B, C.
  8. Optional. Draw a circuit using AND and OR gates, and only two INVERTERS that will invert its three inputs. There are three input lines: A, B, C. The three output lines should have the values: !A, !B, !C. You may use as many AND and OR gates as needed. You may not use any other circuits, such as NAND, NOR, XOR.