Spring 2001, Assignment 1

Due 1/30 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 NAND gates. You may use as many of them as needed. You may ONLY use NAND 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 2, 3, 4, 5.
  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. A 2-bit encoder is a circuit with four input lines, exactly one of which is high at any instant, and two output lines whose 2-bit binary value tells which input is high. Only one of the input lines will ever be active at the same time. You do not have to consider the cases if more than one is active.
    1. (2 points) Draw the truth table for a 2-bit encoder. There will be four input variables and two output variables. Only one of the input varaibles can be 1 at a given time, so there are only 4 possible combinations for valid input variables. Draw the circuit for the 2-bit encoder.
    2. (2 points) Draw the circuit for a 3-bit encoder. There will be 8 input lines and 3 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. (Hint: Vcc, Ground, D, not 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. You may use as many AND and OR gates as needed. You may not use any other circuits, such as NAND, NOR, XOR.