nand2tetris. Memory implementation - memory

Question

I realized Data memory implementation in nand2tetris course. But I really don't understand some parts of my implementation:
CHIP Memory {
IN in[16], load, address[15];
OUT out[16];
PARTS:
DMux4Way(in=load, sel=address[13..14], a=RAM1, b=RAM2, c=scr, d=kbr);
Or(a=RAM1, b=RAM2, out=RAM);
RAM16K(in=in, load=RAM, address=address[0..13], out=RAMout);
Screen(in=in, load=scr, address=address[0..12], out=ScreenOut);
Keyboard(out=KeyboardOut);
Mux4Way16(a=RAMout, b=RAMout, c=ScreenOut, d=KeyboardOut, sel=address[13..14], out=out);
}
Is responsible for what load here. I understand that if load is 0 - out of Dmux4Way in any case will be 0 0 0 0. But i don't understand how it works in that case after that. Namely how it allows don't load data in Memory.
At least incomprehensible why in Screen we fed address[0..12] instead address[0..14] - full address. In my opinion we should use second because Screen memory map stay after RAM memory map and if we want to request for Screen memory map - we should use range (16 384 - 24 575) - decimal or (100000000000000 - 101111111111111) - binary. But how we can represent that range use just 13 width buss (address[0..12]) ??? It's impossible.
Therefore if we want to represent Screen memory map we should use range which was presented above. And that range has 15 width or address[0..14] BUT not address[0..12] (width 13). But why works just address[0..12] and doesn't work address[0..14](full address)
DMux4Way(in=load, sel=address[13..14], a=RAM1, b=RAM2, c=scr, d=kbr);

Answer 1

I'm sorry to criticize you at the beginning, but questions you ask suggest that you didn't do this exercise yourself or didn't start the whole course from the beginning.
To answer your questions:
Ad.1.
You demultiplex a single bit (load bit) to the correct memory part. Thereafter, you then feed the input data to all memory parts at the same time.
It's easier and neater than doing it the other way around, namely, to direct 16-bit input to the correct part (RAM16K, screen, or keyboard) while having a load bit that is connected and active at every register in all the parts.
To clarify. You have 2 possible destinations when writing data: RAM and Screen. The smallest demultiplexer you have is a 4-way multiplexer and that's what you're using. When you write into memory, you need to provide 2 pieces of information: the data and destination, both at the same time.
You might demultiplex the input data with DMux4Way16 and separately single load bit with DMux4Way but that would take 2 demultiplexers, and we can do better than that. That's what's done here, you direct data input to both RAM and Screen and then only use one demultiplexer : DMux4Way to select one of 2 possible destinations, only the one selected will be loaded with new data, on the other data input will be ignored. Knowing that, you need to study A-instruction format: when bit 14 and 13 of A-instruction (or data residing in A-register) have the binary value 00 or 01, the destination is RAM. When bit 14 and 13 have the binary value 10, it means the screen is the destination.
When you notice that you choose these 2 bits as sel for your demultiplexer. Selections 0 and 1 have the same meaning, so you can OR them and feed the output as load to RAM. Selection 2 means Screen will be loaded with a, new value, so load bit goes there. Selection 3 is never used so we don't care about it - output d of demultiplexer will not be connected anywhere. We make use of the demultiplexer's feature: The selected output will have value 1 and all other outputs will yield 0 as a result. It means only 1 memory destination will be loaded.
Ad.2.
Screen is separate device, it has nothing to do with RAM, ROM or Keyboard memory devices here. You, and only you, give meaning to what bits mean what to this specific device. To answer your question, when you address some register in Screen you address it in its own internal address space. In its internal address space first address will be 0, but from whole Memory it will be 16384. It's your job to make this transition. In this particular case, size of Screen memory device it is not necessary to use 14-bit address bus, 13 bits is all you need. What would 14th bit mean in this case? It wouldn't add any value. Also, you are user and not designer of Screen, you only look at and follow its interface description.
Hope it answers your questions, if not I urge you to go back and study more carefully previous hardware related chapters from course.