FourKings wrote
I build the gates from not to mux already, but, the problem is, I build some of them just by trying random combinations of gates that I already have. I dont know how to work out the desired logic base on the given truth table.
What did I miss? Please help!
The simple circuits, up through the Mux and DMux, can be designed algorithmically from their truth tables using the "canonical" form as described in chapter 1. The canonical form can often be simplified using Boolean algebra or Karnaugh maps. See
this post for more info on K-maps.
When you made your Or, you probably discovered one aspect of
De Morgan's Law. it's useful to know in all of its forms.
Canonical form becomes unmanageably complex when more than 5 or 6 inputs are involved.
The 4- and 8-way Muxes and DMuxes can be designed starting with canonical form, but this is harder than designing them using abstraction: think of the N-way Muxes as making a series of choices and build that series of choices using the Mux to make the individual choices. This is analogous to building the Or8Way using a series of Or gates.
Try to get into the mindset that every part you build becomes another tool that you can use to build even more complex parts.
--Mark