srlabib's blog

By srlabib, 15 months ago, In English

Hi All ! Recently I and Noelle-s-Stupidsta 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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7 months ago, # |
  Vote: I like it -6 Vote: I do not like it

Thank you, it helped a lot.

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7 months ago, # |
  Vote: I like it 0 Vote: I do not like it

Third equation is deductible from the second if you apply $$$\oplus a\oplus b$$$ to both sides

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7 months ago, # |
  Vote: I like it +3 Vote: I do not like it

it is helpful