Σ(0,1,3,6,10,12,14) using 8×1 MUX

Use $A, B, C$ as the select lines ($S_2 S_1 S_0$) and the LSB $D$ as the data variable. Data input $I_i$ covers minterm $2i$ (when $D=0$) and $2i+1$ (when $D=1$).

Implementation table (F = Σ(0,1,3,6,10,12,14)):

(Bold = minterm present in F.)

Rules: both entries present gives 1, none gives 0, only the $D'$ row gives $D'$, only the $D$ row gives $D$.

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

Inputs 1 and 0 are tied to $V_{CC}$ and ground; one inverter gives $D'$.

Check: $ABCD = 1100$ (minterm 12) selects $I_6 = D' = 1$, so $F = 1$; $ABCD = 0101$ (minterm 5) selects $I_2 = 0$, so $F = 0$. Both agree with the given function.