Solving Bitwise Arithmetic: What Trick Makes it Easy?

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In summary, the conversation discusses using the properties of bitwise arithmetic, such as the negation and commutative and associative properties of the exclusive-or operator, to easily solve certain problems.
  • #1
tmt1
234
0
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?
 
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  • #2
tmt said:
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?
 
  • #3
Bacterius said:
Finally, ^ is commutative.

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

FAQ: Solving Bitwise Arithmetic: What Trick Makes it Easy?

What is bitwise arithmetic?

Bitwise arithmetic is a type of mathematical operation that operates on individual bits of a number rather than the entire number. It is commonly used in computer programming and digital electronics to manipulate binary data.

What are the basic bitwise operators?

The basic bitwise operators are AND (&), OR (|), XOR (^), NOT (~), and left/right shifts (<<, >>). These operators perform logical operations on the individual bits of two binary numbers.

How is bitwise arithmetic used in computer programming?

Bitwise arithmetic is used in computer programming for tasks such as setting and clearing specific bits, checking if a bit is set or not, and performing logical operations on binary data. It is also commonly used for data compression and encryption.

What are the advantages of using bitwise arithmetic?

Using bitwise arithmetic can result in faster and more efficient code compared to using traditional arithmetic operations. It is also useful for manipulating individual bits of data and performing logical operations on binary data.

Are there any drawbacks to using bitwise arithmetic?

One potential drawback of using bitwise arithmetic is that it can be less intuitive and more difficult to understand compared to traditional arithmetic operations. It also has a limited range of applications and may not be useful for all types of programming tasks.

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