How does using memory with more bits allow you to reduce the address bus

I think W5VO's reply is a great description of a modern memory system but does not really describe Bank Switching.

You want bank switching when you have a narrow address bus (like 8- or 16-bit) and you want to add more memory. You can then use separate GPIO lines to switch memory chips just like W5VO wrote. You have to be careful because all your pointers are still 8-bit and the switching is manual so you can easily cause a mess.

This technique was/is popular in small micros, but also in 16-bit DOS (it was born on the 80286) and kind of in modern 32-bit processors to address more than 4GB of memory (but here the trick is done invisibly by the kernel and one program can still only see 4GB).

Yes, your solutions for the homework are correct. Note that for the 4Mx32 you only use 8 bits per 32 bit word. If you want to use all bits you'd need a 32-to-8 multiplexer/demultiplexer.

#2 and #3 of the lecture are a bit confusing. If the memory is word-addressable with 16-bit words, it's no longer a 4Mx8 memory but a 2Mx16 memory. To address 2M words you need 21 bits. Similar for #3.