4.1-4.2 and 4.4, Due on September 20

I enjoyed reading about the competition in the 1970s that eventually resulted in the design of the DES system. It was fun to read about whether IBM put a trapdoor into the system, or if the NSA put their own trapdoor into the system. Who can you trust when you have someone else come up with a crypto system for you?
Speaking of the DES, if I were to summarize all of my confusion into one word, it would be: Diagrams. I did not follow what was going on in the diagrams or the functions of the DES. I think I could follow most of the particulars if I knew what the big ideas were. I understand that some of the plaintext letters go to more than one ciphertext letters (although not all of them do) but I didn't get the big idea. One of my stumbling blocks is the concept of a 'bit.' Bit seems to have a very loose definition. The book says that a bit is a 1 or a 0. When we talk about a 64 bit key, do we mean the key is a 64 digit number composed entirely of 0s and 1s? It seems that sometimes bits refer to letters, but perhaps what they mean is that a letter is transformed into a number, and that number has only 0s and 1s.