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Here's a calculator you can use to calculate bitwise operations. If you have something more easilty accessible, then by all means use that instead. I think that most people wouldn't have something readily available to do these types of calculations. You can switch between decimal, hexadecimal, and binary. However, one limitation is that it only supports 16-bit values. So you can't enter a value greater than 65,535. This is just to help you understand how certain values in registers, for example, are calculated. Registers are all 16 bits.
This calculator functions like an RPN calculator, so if you're familiar with that (HPs for example), then this will be very familiar. For those who aren't, an RPN calculator needs to have its arguments defined before its operation. For example, if you wanted to do a bitwise "AND" for the two values 134 and 23 you'd first type in 134 and hit "ENTER". Then you'd type in 23 and hit "ENTER". You now have these two values on the "stack". Finally you hit the '&' button to do the bitwise calculation of these two numbers. The second number can also just be in the input box. So you can type in 134, hit "ENTER", then type in 23 and hit the '&' button to get the same result.