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Computer Organization
Computer Science 251
Dickinson College

Spring Semester 1997
TTh 2:00 - 3:15
South College 04

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Homework #3 Solution

Due 2/11/96

• For the following truth tables:
  1. Write the function M in minterm notation.
  2. Simplify the function M using a Karnaugh map.
  3. Write the simplified version of the function M in SOP format.

1. 
   a b c M
   -------
   0 0 0 1
   0 0 1 1
   0 1 0 0
   0 1 1 0
   1 0 0 1
   1 0 1 1
   1 1 0 1
   1 1 1 1
   
   
   
   1. M(a,b,c) = SIGMA(0,1,4,5,6,7)
      
      
   2. 
      
      
   3. M(a,b,c) = A + !B
   
   
   
2. 
   a b c d M
   ---------
   0 0 0 0 1
   0 0 0 1 0
   0 0 1 0 1
   0 0 1 1 0
   0 1 0 0 0
   0 1 0 1 0
   0 1 1 0 0
   0 1 1 1 0
   1 0 0 0 1
   1 0 0 1 0
   1 0 1 0 0
   1 0 1 1 0
   1 1 0 0 1
   1 1 0 1 1
   1 1 1 0 0
   1 1 1 1 0
   
   
   
   1. M(a,b,c,d) = SIGMA(0,2,8,12,13)
      
      There are actually two equally valid (and equally good) solutions to this problem:
      
      
   2. -OR-
      
      
   3. 
      M(a,b,c,d) = !A!B!D + AB!C + A!C!D
      
      -OR-
      
      M(a,b,c,d) = !A!B!D + AB!C + !B!C!D