Fall 2001, Assignment 1

Section 01: Due Tuesday 9/25 at the start of class
Section 02: Due Monday 9/24 at the start of class

  1. (2 points) Draw a circuit for A AND (B OR C) using transistors.
  2. (2 points) Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions. (! is NOT).
  3. (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. When you are done, if there are any gates that are not 2-input NOR gates, then it is wrong.
  4. (4 points) Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 1, 3, 4, 6.
  5. (3 points) Use a PLA to implement the boolean functions from question 2 and question 4. Rename the input variables so that each function uses distinct variables.
  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 3, 6, 7, 8, 10, 13, 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.