How to check if a number is a power of 2 using logical operations[Technique Tuesdays]

A neat little trick for making your computations more effective-

Dec 14, 2022

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Most of you know how to use AND, OR, and NOT operations,

However, very few of you have mastered these operations. Which is a bummer, because these are some super-powerful techniques. Learning to master these will skyrocket your skills, whether it’s in Coding Interviews or just being a better Programmer. Today’s post/email will get you one step closer to that enviable state.

Important Points

What is the technique- Simply put, you can check if a number x is a power of 2 by doing the following comparison-
```
def isPowerOfTwo(x):
    return (x and (not(x & (x - 1)))) 
```
Why does this work- Every power of 2 can be represented in binary by the following regex- 1(0)n [this means 1 followed by n zeroes]. That number-1 is going to be (1)^(n-1) [(n-1) 1s]. So, if a number n is a power of 2 then bitwise & of n and n-1 will be zero. However, x & (x-1) could be 0 if x is 0 (which is not a power of 2). To account for that, we add in the x and portion.
Why this technique is amazing- This is a very important technique because it uses logical operations and bit shifting, which are very computationally efficient. Thus having this technique in your arsenal is a great way to stand out in your interviews/be an effective software engineer.

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