Solving Bitwise Arithmetic: What Trick Makes it Easy?

[tmt1]

1234567 ^ 7 ^ ~~1234567

5 & (12345678 ^ ~~ 12345678)

My prof said there is an easy way to solve these as there is a trick to it. Does anyone know what trick is being referred to?

 

[Nono713]

1234567 ^ 7 ^ ~~1234567

5 & (12345678 ^ ~~ 12345678)

My prof said there is an easy way to solve these as there is a trick to it. Does anyone know what trick is being referred to?

The "tricks" here are just the basic properties of bitwise arithmetic, namely that ~~x is equivalent to x (negating a bit, and then negating it again, gives you back the original bit) and x ^ x is equivalent to 0 (look at the truth table for exclusive-or). Finally, ^ is commutative. Does that make it easier?

 

[I like Serena]

Finally, ^ is commutative.

Nitpicking. We also need that ^ is associative, which it is. ;)