Fall 2002, Assignment 1

Section 02: Due Wednesday 9/25 at the start of class

1. (2 points) Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions. (! is NOT).
   • !ABC + !AB!C + A!BC + AB!C
   • B XOR C
     
2. (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.
   • Draw a circuit diagram for this function using the MSI multiplexer chip on  page 132.
   • Draw a circuit for this using transistors.
   • Draw a circuit for this using SSI chips. Sample SSI chips.
     
3. (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 represented as a binary number. The ouput will be the five 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.
   

4. (3 points) 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. Draw the truth table for a 2-bit demultiplexer. There will be one input variable, two control variables, and 4 output variables.
   2. Draw the circuit for a 2-bit demultiplexer.
   3. Draw the circuit for a 3-bit demultiplexer. There will be one input line, three control lines, and 8 output lines.
      
5. (3 points) 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. 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.
   2. Draw the circuit for the 2-bit encoder.
   3. Draw the circuit for a 3-bit encoder. There will be 8 input lines and 3 output lines.
      
6. (1 point) Using the MSI Multiplexer chip on page132 and one inverter, 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.
   
7. (4 points) The shifter on page 136 only has two functions: shift right and shift left. Create a new circuit that implements a shifter with four functions: arithmetic shift right, don't shift, rotate left, rotate right. The shifting done in the book is logical shifting: a 0 is placed into the S0 or S7 bit, depending on which way the shift goes. An arithmetic shift right places D0 into both S0 and S1: it is duplicating the sign bit. A don't shift operation would send each data bit to the corresponding output: D0 to S0, D1 to S1, etc. A rotate left operation will do a logical shift left and will move the D0 bit to S7. A rotate right operation will do a logical shift right and will move the D7 bit to S0.
   
8. Just for fun: 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.