Questions tagged [boolean]

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Why do we use {+1, -1} in place of {0, 1} for the Fourier analysis of boolean functions?

I want to know what will change if we keep on using {0,1} for our Fourier analysis of boolean functions? What are the things, which can not be performed with {0,1} and can be done with {+1, -1}?
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Karnaugh map and boolean simplification yield unsatisfactory results.[Solved]

My binary logic for my circuit is \begin{array}{|c|c|c|c|c|c|} A &B &C &D &Hallway &Stairs\\\hline 0 &0 &0 &0 &0 &0\\ 0 &0 &0 &1 &1 &1\\ 0 &...
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I am missing something important with Boolean Algebra

It seems that almost every Boolean expression I try and solve, I always find a Boolean Discrepancy . I could go back and use a different property, theorem, or law at different points of the process, ...
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How to solve $(a+bc)(d'+bc)(a'+d')$ using Boolean algebra

I have done this. is this correct? If wrong, what is needed to be changed? $(a+bc)(d'+dc)(a'+d')$ $ = ad'a' + abcd' + bcd'a' + bcbcd'$ $ = d' + abcd' + bcd'a' + bcbcd'$ $ = d' + bcd' (a + a' + bc)$ $ =...
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Probability of a boolean formula which use only xor and and operations

Can I obtain the probability formula from a boolean formula only translating and operator by the multiplication operator; and ...
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Symmetric boolean function in pairs

I am reading this paper "Efficient Algorithms for Computing Differential Properties of Addition". In Lemma2, the authors claim that $$\Delta_{c_{i+1}}=(x_i \land y_i) \oplus (x_i \land c_i) \...
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Simplify Boolean Expression $A\cdot \overline{B\cdot C+C\cdot A}\cdot B$. Where did I go wrong with the simplification

Question Simplify Boolean Expression $A\cdot \overline{B\cdot C+C\cdot A}\cdot B$ My Approach Start $A\cdot \overline{B\cdot C+C\cdot A}\cdot B$ De Morgan's Law $A\cdot(\overline{B}+\overline{C})\cdot(...
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