☯️ XNOR vs NXOR
The gate commonly known as XNOR is logically the negation of XOR, but its name introduces semantic confusion.
Linguistically, “XNOR” implies “exclusive NOR,” which is a contradiction—NOR already implies total exclusion, and cannot be made exclusive.
The correct logical name should be NXOR, following the pattern of NAND and NOR.
✌️ Gates in 2-inputs
| Gate Name | Logical Meaning |
|---|---|
| AND | All True |
| OR | At least one True |
| NOT | Flip Truth Value |
| NAND | At least one False |
| NOR | All False |
| XOR | Opposite Truth Values |
| XNOR | Same Truth Values |
🔍 Gates Generalised
| Gate Name | Logical Meaning |
|---|---|
| AND | All True |
| OR | At least one True |
| NOT | Flip Truth Value |
| NAND | At least one False |
| NOR | All False |
| XOR | Odd Number of Truths |
| XNOR | Same Truth Values |
🚅Derivation of Naming Scheme
OR means both of them included
NOR means not OR, so none of them are included
XOR means only one of them is included at the same time
XNOR should mean only one of them is excluded at one time
🌴Diversion of Linguistics
But that’s not what XNOR means formally, XNOR formally means both of them must be included or excluded
Moreover, logically, only one of them is excluded is the same thing as only one of them is included, which is what we call XOR already
So by the way of naming things, XNOR and XOR should have been the same meaning
⚓ Practical Solution
If we want something that is the opposite of XOR, we will have to negate XOR from the outer scope, which gets us NXOR
NXOR is the logical way the opposite of XOR should’ve been named
🌐 Reality
But XNOR perhaps looked nicer to us than XNOR, so XNOR became to mean what NXOR does mean——inputs are equal