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Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they show different states (not-equal coin sides).

CoinA | CoinB | XOR ("are they different?")
--------------------  
heads | heads | no  
tails | tails | no  
heads | tails | yes  
tails | heads | yes

In boolean terms this would of course map to heads=0, tails=1, no=0, yes=1 for example.

Replace "they" here for "coin sides" or "states" or "inputs" as it seems fitting for the explanation. Maybe it makes it clearer when talking about "are they both/all equal/different" to underline the "exclusiveness" of xor.

This can also (maybe later on) lead to the awareness that not xor ("not different") is the same as "equality" (== operator) with the paraphrasing question "Are they not different (=equal)?". So "all are different" or "all are same" are inverse to each other.

The name has exclusive in it because when xor is yes/1/true, the heads are exclusive. That is, one head excludes the other. This is also true for the tails.

Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they are different (not-equal).

The name has exclusive in it because when xor is yes/1/true, the heads are exclusive. That is, one head excludes the other. This is also true for the tails.

Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they show different states (not-equal coin sides).

CoinA | CoinB | XOR ("are they different?")
--------------------  
heads | heads | no  
tails | tails | no  
heads | tails | yes  
tails | heads | yes

In boolean terms this would of course map to heads=0, tails=1, no=0, yes=1 for example.

Replace "they" here for "coin sides" or "states" or "inputs" as it seems fitting for the explanation. Maybe it makes it clearer when talking about "are they both/all equal/different" to underline the "exclusiveness" of xor.

This can also (maybe later on) lead to the awareness that not xor ("not different") is the same as "equality" (== operator) with the paraphrasing question "Are they not different (=equal)?". So "all are different" or "all are same" are inverse to each other.

Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they show different states (not-equal coin sides).

CoinA | CoinB | XOR ("are they different?")
--------------------  
heads | heads | no  
tails | tails | no  
heads | tails | yes  
tails | heads | yes

In boolean terms this would of course map to heads=0, tails=1, no=0, yes=1 for example.

Replace "they" here for "coin sides" or "states" or "inputs" as it seems fitting for the explanation. Maybe it makes it clearer when talking about "are they both/all equal/different" to underline the "exclusiveness" of xor.

This can also (maybe later on) lead to the awareness that not xor ("not different") is the same as "equality" (== operator) with the paraphrasing question "Are they not different (=equal)?". So "all are different" or "all are same" are inverse to each other.

The name has exclusive in it because when xor is yes/1/true, the heads are exclusive. That is, one head excludes the other. This is also true for the tails.

Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they are different (not-equal).

Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they show different states (not-equal coin sides).

CoinA | CoinB | XOR ("are they different?")
--------------------  
heads | heads | no  
tails | tails | no  
heads | tails | yes  
tails | heads | yes

In boolean terms this would of course map to heads=0, tails=1, no=0, yes=1 for example.

Replace "they" here for "coin sides" or "states" or "inputs" as it seems fitting for the explanation. Maybe it makes it clearer when talking about "are they both/all equal/different" to underline the "exclusiveness" of xor.

This can also (maybe later on) lead to the awareness that not xor ("not different") is the same as "equality" (== operator) with the paraphrasing question "Are they not different (=equal)?". So "all are different" or "all are same" are inverse to each other.