I just wanted to double check that I'm understanding this right from the book, but is a multi-way gate essentially still just a multi-bit gate except only the input has the n-bit wide bus while the output has just one output bit, and the basic goal with making multi-way gates is to perform the same basic boolean operation on n-bits but still end up with a single-bit output for the array of n-bits? So then when it's expanded to a more complex chip like the Mux4Way16, there would be a total of 64 input bits spread across 4 16-bit buses, 2 selector bits, and a single 16-bit output bus?
It happens a lot more than you might think that writing out a question, or telling another engineer about the bug you're trying to fix will focus your thoughts on the problem. Many times have I stopped halfway through describing a bug to a friend because I suddenly realized what was causing it.
The community of engineers at a larger company is one of the things I miss now that I am a working on my own as a consultant.
If I only had a dollar for every forum/StackOverflow message I'd started to write but ended up not posting. Such is the power and value of writing (and discussion); forcing one to think through the problem himself again methodically, a process through which answers are often discovered.