is-power-of-two

Is a power of two

Given a positive integer, write a function to find if it is a power of two or not.

Naive solution

In naive solution we just keep dividing the number by two unless the number becomes 1 and every time we do so we check that remainder after division is always 0. Otherwise the number can't be a power of two.

Bitwise solution

Powers of two in binary form always have just one bit. The only exception is with a signed integer (e.g. an 8-bit signed integer with a value of -128 looks like: 10000000)

1: 0001
2: 0010
4: 0100
8: 1000

So after checking that the number is greater than zero, we can use a bitwise hack to test that one and only one bit is set.

number & (number - 1)

For example for number 8 that operations will look like:

  1000
- 0001
  ----
  0111
  
  1000
& 0111
  ----
  0000    

References

• GeeksForGeeks
• Bitwise Solution on Stanford
• Binary number subtraction on YouTube