I was clear about the concepts explained in the first two lectures of this section: encodings and representation of integers; so, I've not extracted content from those parts.
Regarding to the work with integers in C, the details about signed-unsigned integer casting and automatic sign extension attracted my attention.
Signed-unsigned integer casting
There are explicit and implicit (via assignments and function calls) castings.
In casting between signed and unsigned integers bits are unchanged, just interpreted differently.
Sign extension in C
I studied the floating-point representation in detail some time ago, but this course touches on the floating-point operations too. I extract the three main slides:
Interesting the slide about floating-point types and their casting in C: