Lab 8 Problems: K-Maps with Don't Cares, Multiplexers, and ALUs

---DON'T CARES IN KARNAUGH MAPS (K-MAPS)---

1.)  Given this truth table, find the unoptimized formula this corresponds
to, along with the version which was optimized with a K-Map.

  A B C D | O
  ___________
  0 0 0 0 | 1
  0 0 0 1 | X
  0 0 1 0 | 0
  0 0 1 1 | 1
  0 1 0 0 | X
  0 1 0 1 | 0
  0 1 1 0 | X
  0 1 1 1 | 0
  1 0 0 0 | X
  1 0 0 1 | 0
  1 0 1 0 | 1
  1 0 1 1 | 0
  1 1 0 0 | 1
  1 1 0 1 | 0
  1 1 1 0 | X
  1 1 1 1 | 0

Unoptimized Sum of Products equation
1a) O =

Draw the K-map and simplify
Optimized Sum of Products equation
1b) O =


---MULTIPLEXERS---

For your answers for this part, put your answer on the SAME LINE as the
prompt.  For example:

What is 2 + 8?
ex) 10


2) Using only AND, OR, and NOT gates, construct a 2-input multiplexer (MUX).
The inputs to the multiplexer should be A, B, and S, where S is the
selector.  Draw the circuit and include it in your submission as
"lab8smallmux.jpg".


3) An 8-input MUX can be constructed entirely with 2-input MUXes.
I will start you out - put inputs A and B into one MUX and inputs C and D
into another MUX. Continue on with E F and G H like this.
This is the first stage of the solution.
Then decide how to reconcile the two results from those MUXes.
Think hard about the logic for a 2-input MUX vs an 8-input MUX.

How many 2-input MUXes are needed to create an 8-input MUX?
3a)

How many select lines are needed?
3b)

Draw the circuit and include it in your submission as "lab8bigmux.jpg".


---ARITHMETIC LOGIC UNITS (ALUs)---

The first problem of step 1 of Lab 7
(https://kyledewey.github.io/comp122-fall17/labs/lab_7/)
required you to write out the truth table for addition with a single bit.
The questions below build on top of that work.


What is the unoptimized sum-of-products formula corresponding to R?

4a) R =

Draw a K-map and simplify the formula above.
Optimized Sum of Products equation:

4b) R =


What is the unoptimized sum-of-products formula corresponding to Cout?

4c) Cout =

Draw a K-map and simplify the formula above.
Optimized Sum of Products equation:

4d) Cout =

Draw the circuit corresponding to Cout and include it in your submission
as "lab8cout.jpg".  You do NOT need to draw the circuit for R as it is
prohibitively large.