How to create K-MAP from function

Question

How can I create a K-MAP by looking at this function.I dont know how to create one

Answer 1

Create the truth table, from that create the K-MAPs (Karnaugh maps), from that create the booleans, from that create the CKTs. One of the 6 outputs, Y5 (Y=f(x)), is completed below ...

           Truth Table
           ------------
4s 2s 1s      32s 16s 8s 4s 2s 1s
X2 X1 X0 # | #  Y5 Y4 Y3 Y2 Y1 Y1
0  0  0  0 | 0  x  x  x  x  x  x  [1]
0  0  1  1 | 0  0  0  0  0  0  0 
0  1  0  2 | 2  0  0  0  0  1  0
0  1  1  3 | 6  0  0  0  1  1  0
1  0  0  4 | 12 0  0  1  1  0  0
1  0  1  5 | 20 0  1  0  1  0  0
1  1  0  6 | 30 0  1  1  1  1  0
1  1  1  7 | 42 1  0  1  0  1  0
    [1] 0 input is not positive so is not allowed, so we "don't care" about these outputs


           Y5 K-Map
           --------
X2  \ X1 X0  00 01 11 10
     \
0            x  0  0  0  
1            0  0  1  0


           Y5 Boolean (Product of Sums in this case, Sum of Products is another option)
           ----------
Y5 = X2 ^ X1 ^ X3 = (X2 ^ X1) ^ X3



           Y5 Circuit
           ----------
      ______
X2 ---|     |
      | AND |---|   ______ 
X1 ---|_____|   |---|     |
                    | AND |--- Y5
X2 -----------------|_____|



Etc...