Q:

What is the benefit of studying bitwise operators?

What is the benefit of studying bitwise operators (Bitwise Not, Bitwise AND, Bitwise OR, Bitwise XOR, Left Shift, Signed Right Shift, Unsigned Right Shift etc.)?
Will we really use these operators in programming?

A:

"Yes, we will."
Bitwise operations are everywhere. They are perfect for working with bitfields (a practice that is ubiquitous in C and C++), such as a 'flags' field in a data structure or function argument. Basically, | combines flags, ^ flips flags, & checks if a flag is set, and the x &= ~FLAG pattern clears a flag.
Bitwise operations are ubiquitous in all things low-level - hardware drivers, network protocols, binary file formats - as well as some higher-level fields like character encodings, cryptography, etc.
Bit-shifting can also sometimes double for integer division and multiplication by powers of 2, with a slightly different rounding behavior for negative numbers (sometimes, but not always, more desirable than what regular integer division does).
In tight loops, bitwise arithmetic can sometimes be used to avoid conditionals, which is beneficial because modern CPUs use branch prediction, and a misprediction (i.e., the condition in an if statement evaluates differently from the previous time) causes a significant delay. Using bitwise arithmetic, the same calculation can sometimes be expressed without any conditionals.
Even if you don't intend to work in any of the above scenarios, it is still a good idea to study and understand bitwise operations - all modern computers are binary, and you definitely need to know the basic principles by which they operate. Numbers in a computer don't behave like numbers in the real world, and studying binary operations will help you understand why.

A:

It all depends on what your focus is really. Some programmers may go their entire career without using bitwise operations and may do quite well for themselves (although they will encounter frustration whenever dealing with code that contains them).
However, bitwise operations are a fundamental part of software engineering and questions pertaining to them are asked quite frequently in interviews (along with other fundamental CS questions such as how to convert between base-x and base-y).
You'll find that those who come from a CS background will use them when the need arises in many different ways (a common use case is a bit field). If you don't understand how bit operations work, you'll generally be at a loss trying to understand the sections containing them.
Now, having said all that, bitwise operations should be fairly easy to understand for anyone pursuing a career in programming and shouldn't really require a lot of studying.

A:

I work in the embedded field and being completely at home with bitwise operations is a sine qua non for anyone that wants to work here.  It is one of the first interview questions that I ask.  All of our software has a very intimate relationship with the hardware most of which is controlled by modifying single bits in hardware registers.  Changing the wrong bit has disastrous consequences.

