CSc 4250/6250 Homework #2
Date assigned: September 22, 2005
Date due: September 29 or October 6 (we will decide in class)
This homework is an individual homework.
You are expected to do all work on your own.
Suppose you have the following 4-variable function:
f = Sigma(0, 4, 6, 8, 9, 10, 11, 15)
1. Show how you would reduce this using a Karnaugh map. What is the
final expression for f?
2. Draw function f with 2-input AND, OR, and NOT gates only.
3. Take your answer from #2 and convert it to 2-input NAND gates only.
4. How would you draw a circuit for the function f4 below,
in terms of N and P transistors? Assume double-rail logic.
f4(a,b,c,d) = prime number bit.
For example, if abcd=0100, then f4=0 (a is the most significant bit).
If abcd=0101, f4=1. NOTE: this was corrected 9/25/05.
You should consider 0 or 1 to be a prime number (OR in the logical sense) in
order to make your circuit easier to implement. But you must explicitly
say whether you consider 0 to be prime and whether you consider 1 to be
prime (and show how it makes things easier).
5. Suppose you had the following gates drawn (correctly!) in Magic:
a 2-input NAND, a 2-input NOR, and an Inverter. Implement the following
function in terms of these gates. Assume the gates are cells, and that
you just have a box with inputs at the top and an output at the bottom.
All you have to do is show how the connections are made. Be sure to
label the cells appropriately.
Note: You do not have to implement these in Magic, just on paper.
Treat each gate as a box with
inputs (including Vdd!) running in metal1 across the top,
and outputs (as well as GND!) running in metal1 across the bottom.
Be sure to specify connections between inputs and outputs.
f5 = a'd' + bc'd + ab'cd
6. Drawn 3-input NAND and NOR gates on paper, as they would appear in Magic.
Use colored pens/markers.
7. Draw a 4-1 MUX using N-SWITCHES and P-SWITCHES.