Σ(0,2,3,6,7,8,12,13,15) using 8×1 MUX

Use $A, B, C$ as select lines ($S_2S_1S_0$) and $D$ (LSB) as the data variable. Input $I_i$ corresponds to minterms $2i$ (with $D=0$) and $2i+1$ (with $D=1$).

Implementation table for $F = \Sigma(0,2,3,6,7,8,12,13,15)$ (bold = minterm in F):

Rule: both entries bold gives 1, neither gives 0, only the upper ($D'$) row gives $D'$, and only the lower ($D$) row gives $D$.

Circuit:

D' --> I0 +--------+
1  --> I1 |        |
0  --> I2 |  8x1   |
1  --> I3 |  MUX   |--> F
D' --> I4 |        |
0  --> I5 |        |
1  --> I6 |        |
D  --> I7 +--------+
           S2 S1 S0
           A  B  C

Logic 1 is tied to $V_{CC}$, logic 0 to ground, and a NOT gate gives $D'$.

Verification:

All agree with the given minterm list, so the function is realized with one 8×1 MUX and one inverter.