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 XOR B using transistors.
2. (2 points) Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions. (! is NOT).
   • !A!BC + !AB!C + A!BC + AB!C
   • B XOR C
     
3. (2 points) Draw a 4-to-1 multiplexer 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. When you are done, if there are any gates that are not 2-input NAND 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 2, 3, 4, 5.
   • Draw a circuit diagram for this function using only NOT, AND, and OR gates. (Hint: simplify it first).
   • Draw a circuit diagram for this function using the MSI multiplexer chip on  page 132. (Hint: do NOT simplify it first!)
     
5. (3 points) A computer store has five upgrade packages. They are numbered as 0, 1, 2, 3, 4. There are five different devices that can be added: LCD Monitor, Extra RAM, DVD, Ethernet Card, or Modem. Below are the possible configurations for the upgrade pacakges.
   

   Package	LCD Monitor	Extra Rom	DVD	Ethernet Card	Modem
   0	Yes	No	Yes	No	No
   1	No	Yes	Yes	Yes	No
   2	Yes	No	Yes	No	Yes
   3	No	No	No	Yes	Yes
   4	Yes	Yes	Yes	Yes	Yes

   
   Implement this using a PLA. The input to the PLA will be the package number. The ouput will be the possible devices. Draw all the lines that you use into each AND gate (6 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, 2, 7, 9, 12, 14, 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.