The logic of designing a HDL parts from the beginning : DM

I am taking the nand2tetris coursera course. I am trying to understand how you guys, can design the underlying mental process of finding the HDL core parts. For exemple, let's take the DMUX4way. What is the complete mental process to achieve the parts? I understand the logic behind once I see the result but I have difficulties to find out by myself Thanks

    * {a,b,c,d} = {in,0,0,0} if sel==00
     *             {0,in,0,0} if sel==01
     *             {0,0,in,0} if sel==10
     *             {0,0,0,in} if sel==11
     */
    
    CHIP DMux4Way {
        IN in, sel[2];
        OUT a, b, c, d;
    
        PARTS:
        DMux(in=in,sel=sel[1],a=ao,b=bo);
        DMux(in=ao,sel=sel[0],a=a,b=b);
        DMux(in=bo,sel=sel[0],a=c,b=d);
}

I find that it helps to break things down, and in complex situations, write down the truth table for the various signals (including the intermediate signals). Sometimes this will lead to an "aha" moment where you see a connection you can use to simplify things.

You may also find it helpful to draw a graph that maps the flow of the signals through the circuit.

Finally, the adage that "first make it work, then make it pretty" applies. Once you have something working, you can look at the design and find simplifications and optimizations. A good example of this is building the XOR circuit. Once you have the straightforward version, if you look at it hard, you can find the clever optimization.

I suppose it is just one of those things where you have to practice until you get the knack of it. You may find it useful to revisit earlier projects with an eye to making them cleaner and easier for you to understand. There are often several ways to build the required circuit, but some ways may be more comprehensible to you. Also, I would recommend you get in the habit of commenting your designs; it is helpful to have a reminder what you were thinking when you did something.