I still often encounter people with a Master's degree in Computer Science, Information Technology or whatever, who are not used to think bits and bytes. The world of computing is huge, and I fully understand that the universities need to filter and carefully select what topics they should teach their students. However, there is a huge number of topics where knowledge about bit manipulation is important: IT security, resource leaks, format compatibility, communication protocols, low level APIs, data conversion, and even such thing as understanding UTF-8 used in XML, and many other places. There almost isn't a problem that cannot be understood by looking at it as bits and bytes.
Therefore, my advice to Computer Science students is this: Learn and understand bits and bytes, addressing, data formats (including IEEE 754!), binary operators and pointers and offsets. Don't consider yourself a good programmer before you know these by heart.