I have partial understanding of how to deduce the chip implementation. But I am still uncertain of how to use the algebra well.
K-maps or canonical forms I have tried to make sense of.
in=Not(sel)AND(a)OR so 0=(0.a)
in=(sel)AND(b) so 1=(1.b)
You seem to be confusing inputs and outputs. In the DMux, you have an input signal called 'in', and input signal called 'sel', and two output signals called 'a' and 'b'. So your logic equations should be of the form
I watched some internet tutorials, but still my understanding of mathematics is inadequate; I'll work on that. But in my previous thoughts I reasoned two And chips could give different 'a' and 'b' outputs; because 1 and 1 will give 1; and 1 and 0 will give 0. And I thought there's got to be a Not chip to make this happen. But I wasn't creative enough to wire it.
But the thing that I now understand is you can apply the truth tables to the input values, to get a start on the implementation. I had the right idea from the outputs back, but not from the inputs forward.
I had an over complicated idea of the input values.