Bit Manipulation

Number of bit to be flipped to convert one number to another.

Objec­tive:  Given two numbers x and y. write an algorithm to find the number of bits which are to be flipped to convert number x to y.


x = 10, Y = 20
x = 0 1 0 1 0, y = 1 0 1 0 0
So if we need to convert x to y then a) turn on the bits at 2nd and 5th position b) turn off the bits at 1st and 4th position.
Output: 4


Let’s observe the XOR table

  • So as we can see that XOR of two numbers will set the bit in result if the bit is set in either in X or Y, not in both.
  • Calculate z = x XOR y.
  • Count the number of set bits in z. this will be the final answer.



Number of bit needs to be flipped to convert 10 to 20 are: 4

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