Problem Detail: Suppose that $Z = X vee Y$, where $X$, $Y$ and $Z$ are 96-bit binary numbers. If I’m given the values of $Z$ and $Y$, is it possible to work out what $X$ is? I know this is possible with XOR but can it be done with OR?
Asked By : SHdotCom
Answered By : beginner1010
It is easy to find out that there can be more than one value, used as $X$, to satisfy $Z = X vee Y$. When a specific bit of $Y$ is $1$, there are two possibilities for such bit in $X$, i.e., $0$ or $1$. Let’s make a simple example with a 2-bit number: $Y$ = $10$ and $Z$ = $11$ The possible values of $X$ are:
- $11$
- $01$
because:
- $11 vee 10 = 11$
- $01 vee 10 = 11$
In short, you don’t have the certainty that the end result of the reverse operation of $vee$ will be a unique result.
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