SWE 637 Quiz Number 8
March 26, 2012

Consider the following boolean function 

   f = ab + bc
   // In Java:  a && b || b && c
  1. Draw two K maps, one for f and one for ~f, the negation of f 
      f  \       ab               ~f \       ab
      \ 00  01  11  10            \ 00  01  11  10
       -----------------            -----------------
 c   0 |   |   |   |   |      c   0 |   |   |   |   |
       -----------------            -----------------
     1 |   |   |   |   |          1 |   |   |   |   | 
       -----------------            -----------------


    Answer:
    For f: 
         \       ab
      \ 00  01  11  10
       -----------------
 c   0 |   |   | t |   |
       -----------------
     1 |   | t | t |   |
       -----------------

    For ~f 
         \       ab
      \ 00  01  11  10
       -----------------
 c   0 | t | t |   | t |
       -----------------
     1 | t |   |   | t |
       -----------------
  2. Find a minimal representation for ~f.
    Answer: 
       ~f = ~b + ~a~c
  3. For each implicant in f and ~f, find all unique true points (UTPs). List UTPs by implicant.

    Answer: 
    For f
   for ab     TTF
   for bc     FTT
For ~f
   for ~b     TFF, FFT, TFT
   for ~a~c   FTF
  4. Find a CUTPNFP test set for f. Hint: There is only one possible answer.
    Answer: 
    For implicant ab:
   Select UTP TTF.
   For literal a, select NFP FTF
   For literal b, select NFP TFF
For implicant bc:
   Select UTP FTT.
   For literal b, select NFP FFT
   For literal c, select NFP FTF
    Hence the CUTPNFP set is the two UTPs plus the three NFPs: {TTF, FTT, FTF, TFF, FFT}.
Grading note: I'll accept test inputs identified explicitly, as above, or simply identified on the K-map in some unambigious way.