Creating the HDL code for the OR gate and MUX gate

[asilvester635]

I have questions relating to the simplification of the OR gate and MUX gate. Below is a screen shot for both gates.

Question:
- Or gate: The simplification is from nand2tetris Wiki. How was the simplification done? All the other gate simplifications were done step by step, but not for this one (see image below).

- Mux gate: How is ‘b+b = 1? This is underlined in red. (see image below)

[ybakos]

When figuring out OR, I first thought, "how can I make an OR from a canonical representation that already includes OR itself?!" I looked at different basic boolean proofs, and then I stumbled across DeMorgan's law.

Take a look at DeMorgan's Law, and see what you can apply to each side to isolate "A+B = .....".
This would express that "OR is equivalent to...."

[cadet1620]

asilvester635 wrote

I have questions relating to the simplification of the OR gate and MUX gate. Below is a screen shot for both gates.

Question:
- Or gate: The simplification is from nand2tetris Wiki. How was the simplification done? All the other gate simplifications were done step by step, but not for this one (see image below).

- Mux gate: How is ‘b+b = 1? This is underlined in red. (see image below)

I know of no "nand2tetris wiki". Googling for that turns up a student's page that appear to be what you found.

As ybakos said, De Morgan's Laws are how to get to the Not/Nand solution for Or.

x+~x = 1 and x(~x) = 0 are fundamental theorems of Boolean algebra.

In general, simplifying cannonical representations using algebra is a lot of extra work!
You want to learn about "Karnaugh Maps".  Search the forum for information about them.

--Mark