COMP 150 Gates Homework

This is an individual assignment, not a pair assignment.

If you turn in the assignment on paper, include the usual log questiions (other than the partner ones).  If you turn this in online, include the log comments in log.txt (minus the partner part).

You may write it on paper and scan it before uploading online.

1. (5 points) Create circuit diagram for the Boolean expression (AB + C)D.
2. (5 points) Write a Boolean expression for the output of this circuit:

Remember wires only connect at dots.
3. (5 points) Write a Truth Table for the Boolean expression (A+B')C.  Include columns for the inputs A, B, and C.  Please include a column in your truth table for the output of each intermediate expression.  Include rows for all 8 combinations of input variables.
4. (5 points)  A three-way majority circuit is one with three inputs and a single output which is set to the majority value in the three inputs (output 1 with two or more 1 inputs; output 0 with two or more 0 inputs).  With three inputs there are eight possible combinations for the input settings. Please give a truth table which lists rows for all eight input combinations along with the output that should be associated with each case.
5. (5 points)  Write a Boolean expression for the output of the three-way majority circuit from problem 4.
6. (5 points)  Construct a circuit which implements the three-way majority function discussed in the previous two questions.  You may use AND and OR gates with more than 2 inputs to make it easier.
Submit  in Sakai.  (Include the extra credit portion below if you like.)  You have presumably drawn some pictures.  If they are on paper, scan your work into a computer computer file.  You will need to submit a modified log.txt (no reference to a partner).

Extra Credit A. (5 points)

Interestingly, any given boolean function can be calculated by a circuit consisting solely of NAND gates.
• Create a circuit, using only NAND gates, which has the same overall behavior as a NOT gate. Your circuit should have one input and one output .
• Create a circuit, using only NAND gates, which has the same overall behavior as an AND gate. Your circuit should have two inputs and one output.
• Create a circuit, using only NAND gates, which has the same overall behavior as an OR gate. Your circuit should have two inputs and one output.
• Extra Credit B. (5 points)

Consider the component with the M2 symbol at the left, above.  M2 is the symbol that I give for a multiplexer with two control lines, C0 and C1on the bottom, with the least significant bit to the left (C0),  and with four data input lines on the left, D0 - D3, with lines for data bits 0-3 going down from the top, and the single output line on the far right.  Complete the circuit diagram started below, to create an M4 multiplexer circuit.  At this point all that is shown are the four control lines, at the bottom, least significant bit at the left,  and 16 data input lines on the left with lines for data bits 0-15 going down from the top, and one output line at the far right.  Draw in five of these M2 multiplexers, lots of wires, and no other gates, to correctly connect these inputs and output.  Be sure to draw a clear dot where you mean two wires to connect.  (Hint: look at the relationship between the circuit diagrams in the notes for the multiplexer with one control line and the multiplexer with two control lines.)