3. A 3-line to 8-line decoder is connected as shown. Where x, y and z are inputs (z is the least significant input digit) and F is an output. Which of the following expressions correctly describes F?

  1. F(x,y,z) = z
  2. F(x,y,z) = x
  3. F(x,y,z) = z'
  4. F(x,y,z) = yz
  5. F(x,y,z) = x'




4 is CORRECT. By inspection F = m3 + m7. K-map exploitation then leads to the result F(x,y,z) = yz, as shown as follows: 



                     ____x____ 

          _____________________ 

          |   0|   2|   6|   4| 

          |    |    |    |    | 

          |____|____|____|____| 

         ||   1|   3|   7|   5| 

        z||    | 1  | 1  |    | <- Group this cell of two

         ||____|____|____|____|    to obtain F = yz

                _________ 

                              y

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