Solving the first part gave me 216.667 us. I would double check your math there.
$$100000 \cdot 1.3 = 130000$$
$$\frac{130000}{600 \cdot 10^6} = 2.167 \cdot 10^{-4}$$
Using this gives you the correct solution.
Nothing tells 01100001 (61h) is an ASCII binary representation of letter 'a'... except the context. In a computer what a sequence of bits such as 01100001 represents depends on where it's found and how the container is structured.
In a file organized in bytes, you'll mostly find alphabetic characters represented in a continuous flow of 8-bit characters in text files, for instance. Now whether 01100001 represents the letter "a" depends on what standard the containing text file conforms to; "a" is represented 61h in ASCII and 81h in EBCDIC, to name only two.
This is a simplistic explanation as there's also page codes, which were invented because 256 positions is not enough to represent international alphabets. For text files, operating systems have character encodings, each of which defines how (and what) characters are translated into what binary representation.
ASCII is one of them and uses only 256 positions for [some of] English alphabetic and non alphabetic, numbers, [a limited set of] punctuation and [non printable] control characters. ISO-8859-1 is a variant of ASCII which accounts for several European accented characters. UTF-8, another one of them defines a variable-length byte representation to account for the representation of most characters in all languages.
On a UNIX system like GNU/Linux, what character encoding a text file follows is shown by its MIME type. See GNU/Linux command file -i
# file -i dead.letter
dead.letter: text/plain; charset=us-ascii
This shows file dead.letter is a text file that uses ASCII for its content. In such file types 01100001 (61h) represents the letter "a". The MIME type of a text file is determined (read: set) automatically by the editor that saved the file, depending on the locale (aka regional settings) the editor was started. The MIME type can be saved to disk along with the text file or guessed at run-time from the file content when the file is read. The latter is true especially when reading from GNU operating systems files that were saved in Windows as the latter defines no such thing as MIME types.
Again, this is a summarized explanation but that's the base.
Best Answer
In a computer, "bits" as you say generally move through the computer in parallel busses corresponding to the word length of the computer, which might be 8, 16, 24 or 32 bits (earlier computers also used other values like 12, 18 and 36).
At various points in the computer, these signals are get stored in registers, which are typically made up of flip-flops. Here is a simple set-reset (SR) flip-flop made up of two NAND gates (NAND stands for NOT AND). For a register containing 8 bites (one byte), there would be 8 of these flip-flops. (In reality, the flip-flops used would typically be made up of a more complex circuit, but the concept is the same.) So each bit of the register is kept separate (the Q leads are the positive outputs).
Each of these NAND gates is made up of transistors. Here is a simplified circuit for one NAND gate using MOSFET transistors:
The two inputs A and B correspond to the two inputs going into the symbolic NAND gate as shown in the first drawing above. The Y lead corresponds to the Q lead of the first drawing.
There are four transistors. True, each input A and B is connected to the gates of two transistors. That is done to facilitate the operation of the gate, as I have described in another answer here. It doesn't mean the bits are connected together -- I'm not sure where you got that idea. Remember, one bit is represented by the entire flip-flop, made up of two of these NAND gates, or eight transistors total.