Alternate form of $(A \oplus B)^c$?

Asked Apr 15 '16 at 16:22

Active Apr 15 '16 at 17:33

Viewed 61 times

What alternate forms are there of this equation?

$$(A \oplus B)^c$$

$A$ and $B$ are binary vectors / integers, $\oplus$ is the bitwise XOR operator, $c$ is a constant. For example:

$$(5 \oplus 7)^2 = ((1, 0, 1) \oplus (1, 1, 1))^2 = ((0, 1, 0))^2 = 2^2 = 4$$

By definition, it's the same as this:

$$(\sum ((a_i + b_i \bmod 2) \cdot 2^i))^c$$

Is there another formula which doesn't require an aggregate like $\sum$?

edited Apr 15 '16 at 17:33

Kamil Jarosz

asked Apr 15 '16 at 16:22

Matt Thomas

2

Gah! Don't use set brackets ${\cdots}$ when you're talking about sequences! Sets don't have order, and don't distinguish between containing an element one or multiple times. – hmakholm left over Monica Apr 15 '16 at 16:27
Possible duplicate of How to represent XOR of two decimal Numbers with Arithmetic Operators – Apr 15 '16 at 16:28
@HenningMakholm Thanks! I edited to fix that – Matt Thomas Apr 15 '16 at 17:26
1

@AhmedS. I think that other question has to do with $A \bigoplus B$ not $(A \bigoplus B)^c$. Also, the answers all require $\sum$ – Matt Thomas Apr 15 '16 at 17:29

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