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Is there any way to represent XOR of two decimal Numbers using Arithmetic Operators (+,-,*,/,%).

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    What is the definition of the XOR of two decimal numbers?2011-09-03
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    @Rickey Demer: Thanks for bringing this question. My actual Question should be like this ?2011-09-03
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    @Ricky, every natural number is the sum of different powers of 2 in exactly one way; this establishes a bijection between $\mathbb N$ and the set of finite subsets of $\{1,2,4,8,...\}$. Then bitwise XOR is the binary operation on natural numbers that corresponds to the operation $(A,B) \mapsto (A\cup B)\setminus(A\cap B)$ on sets-of-powers-of-2.2011-09-03
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    I believe the question actually concerns two numbers represented in binary, not decimal numbers as the title says.2011-09-04
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    i want the formula for xor of two decimal numbers using arthimetic operators made up of decimal numbers2011-09-04
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    @Sunny Does the formula have to work for *any* pair of decimal numbers, or can it work for a particular pair like (0, 1)?2011-09-04
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    the formula should have to work for any pair of decimal numbers. in this way we will derive square of two numbers x and y (x+y)2=x2+y2+2xy in the same way is there any formula for x^y=(?) the right side equation(?) should be constructed with x,y and with some algebra.2011-09-04
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    possible duplicate of [Expressing bitwise operations in terms of other functions](http://math.stackexchange.com/questions/15141/expressing-bitwise-operations-in-terms-of-other-functions)2011-10-04

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