Question on digital DE-MULTIPLEXER!
It's just AND gates.  So, assuming $in$ is the input, $sel$ is your selector bit, and $out_1$ and $out_2$ are your two possible outputs, you would get:

$out_1 = in \land \lnot sel$

$out_2 = in \land sel$

The idea is that, if $in$ is $0$, out must always be $0$.  If $in$ is $1$, then we have to output it to the proper gate.   If you had a larger demux, you would simply have more selector bits.  So, for a demux with 16 outputs, we would need 4 selector bits: $sel1$, $sel2$, $sel4$, and $sel8$.  Output 10 would thus be a 5-input AND gate:

$out_{10} = in \land (sel_8 \land \lnot sel_4 \land sel_2 \land \lnot sel_1)$

The other outputs would be blocked because they would have different combinations of $sel1$, $sel2$, $sel4$, and $sel8$ ANDed into their outputs.