Spring 1999, Assignment 1

Due 2/3 at the start of class

1. (2 points) Redraw the multiplexer circuit on page 131 using 2-input NAND gates. You may use as many of them as needed.
   
2. (2 points) Consider the three input boolean function that is 1 if the binary equivalent of the inputs is 0, 3, 5, or 6. Draw a circuit diagram for this function using the MSI multiplexer chip on  page 132.
   
3. (2 points) Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 0, 4, 6, 7. Draw a circuit diagram for this function using the MSI multiplexer chip on  page 132. (Hint: simplify it first).
   
4. (2 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 and D, E, F).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.
   
5. 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. (2 points) Draw the truth table for a 2-bit demultiplexer. There will be one input variable, two control variables, and 4 output variables. Draw the circuit for the 2-bit demultiplexer.
   2. (2 points) Draw the circuit for a 3-bit demultiplexer. There will be one input line, three control lines, and 8 output lines.
      
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.
   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 states for the 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. (2 points) Using the MSI Multiplexer chip on page132, implement the 4-input majority function. Label the 4 inputs as A, B, C, and D. (Hint: Vcc, Ground, D, not D).
   
8. (2 points) (Page 200, #18) A 16-bit ALU is built up of 16 1-bit ALUs, each one having an add time of 10 nsec. If there is an additional 1 nsec delay for propagation from one ALU to the next, how long does it take for the result of a 16-bit add to appear? (Yes, this is a gift.)
   
9. 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. No NAND, and no NOR gates may be used.