srlabib's blog

Some equations using bitwise operators!
By srlabib, 4 years ago, In English

Hi All ! Recently I and turzo_sawroop have done some observations on bitwise operations and found these equations and properties that you may find helpful. I want to share them with you in a nutshell. Here is a shortlist of them:

Some properties of bitwise operations:

  • a|b = a⊕b + a&b
  • a⊕(a&b) = (a|b)⊕b
  • b⊕(a&b) = (a|b)⊕a
  • (a&b)⊕(a|b) = a⊕b

Addition:

  • a+b = a|b + a&b
  • a+b = a⊕b + 2(a&b)

Subtraction:

  • a-b = (a⊕(a&b))-((a|b)⊕a)
  • a-b = ((a|b)⊕b)-((a|b)⊕a)
  • a-b = (a⊕(a&b))-(b⊕(a&b))
  • a-b = ((a|b)⊕b)-(b⊕(a&b))

Hope you like it. Please let me know if you find any issues. All of these properties are elaborated in this blog here. You can also check it out to learn more!

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Comments Comments (10)
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3 years ago, # |
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Third equation is deductible from the second if you apply $$$\oplus a\oplus b$$$ to both sides

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3 years ago, # |
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it is helpful

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19 months ago, # |
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This is helpful for solving this problem, https://codeforces.me/problemset/problem/1556/D Thank you srlabib and turzo_sawroop!!

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22 hours ago, # |
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thanks bro solved C in today's contest using one equation from here

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    21 hour(s) ago, # ^ |
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    which one did you use?

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      21 hour(s) ago, # ^ |
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      a + b = a ^ b + 2 (a & b)

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      21 hour(s) ago, # ^ |
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      the 2nd addition eqn . Making a&b == 0 .

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        11 hours ago, # ^ |
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        if a = x + k and b = y + k what is the approach now , how do i find k?

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          11 hours ago, # ^ |
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          Just make the maximum of x+k and y+k equal to $$$2^n>10^9$$$. This will make the smaller one of the two less than $$$2^n$$$, making the '&' operation's result be 0.

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22 hours ago, # |
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very useful

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