Function Σm(0,2,3,5,7,8,10,13,15) using 1:8 DEMUX

A 1:8 DEMUX with data input tied to 1 produces the 8 minterms of its three select variables. The 4-variable function is realized by choosing three variables as selects and handling the fourth with a gate.

Choice of select lines

Use $B, C, D$ as selects ($S_2 S_1 S_0$) and the data input $= 1$. Then output $Y_j$ is 1 when $BCD = j$. Each $Y_j$ covers two minterms of the function: $j$ (with $A=0$) and $j+8$ (with $A=1$).

Hence

$$Y = Y_0 + Y_2 + Y_5 + Y_7 + A'Y_3$$

Circuit

            +---------+
   1 ------>| D    Y0 |-------> Y0
            |      Y1 |         (not used)
  B --->S2  |      Y2 |-------> Y2
  C --->S1  | 1:8  Y3 |-------> Y3
  D --->S0  |      Y4 |         (not used)
            |      Y5 |-------> Y5
            |      Y6 |         (not used)
            |      Y7 |-------> Y7
            +---------+

  A ---[NOT]--- A'
  A', Y3 ---[AND]--- A'Y3

  Y0, Y2, Y5, Y7, A'Y3 ---[OR 5]---> Y

Gates: one NOT (for $A'$), one 2-input AND ($A'Y_3$) and one 5-input OR.

Check: minterm 11 ($A=1, BCD=011$): only $Y_3 = 1$, but $A' = 0$, so $Y = 0$ (correct, 11 is not in the list). Minterm 3 ($A=0$): $A'Y_3 = 1$, so $Y = 1$. All nine minterms 0, 2, 3, 5, 7, 8, 10, 13, 15 give $Y = 1$.

(For reference, the minimal SOP is $Y = B'D' + BD + A'B'C$, which matches the result above.)