12. Which of the following expressions is the only correct canonical representation for the function F(x,y,z) = y?

  1. F = SUM m(0,1,4,5)
  2. F = SUM m(0,1,2,3)
  3. F = SUM m(4,5,6,7)
  4. F = SUM m(1,3,5,7)
  5. F = SUM m(2,3,6,7)

5 is CORRECT. First draw a truth table for F: 

x  y  z  |  F=y 
---------+----
0  0  0  |  0 
0  0  1  |  0
0  1  0  |  1 -minterm
0  1  1  |  1 -minterm
1  0  0  |  0
1  0  1  |  0
1  1  0  |  1 -minterm
1  1  1  |  1 -minterm
Observe that there are 4 minterms in rows 2,3,6 and 7.

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