Digital Logic Toolkit

Digital Logic Toolkit — XOR gate

Source
https://digitallogictoolkit.com/xor-gate/
Printed

Full 2-input truth table — XOR gate

introtrue when the inputs differ

Answer

output column 0110

Why this example is worth doing

The defining reading: XOR outputs 1 when its inputs are unequal, which makes it a one-bit difference detector rather than a kind of OR. Every use it has follows from that — comparison, parity, controlled inversion, addition without carry. The page leads with the inequality description and gives the or-but-not-both description second, because the first generalises to more inputs and the second does not.

Try your own input in the XOR gate. Truth table, symbol and algebraic form for A ⊕ B, the difference detector.

How the answer is reached

Truth table

Truth table — columns #, A, B, A ⊕ B
#ABA ⊕ B
0000
1011
2101
3110

Compare with

Open the XOR gate

This input is entered in the tool itself — it is too rich for a link to carry.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • Gate symbols follow whichever standard the header toggle is set to: ANSI/IEEE Std 91-1984 distinctive shapes, or IEC 60617-12 rectangles.

Sources

  • ANSI/IEEE Std 91-1984, Graphic Symbols for Logic Functions
  • IEC 60617-12, Graphical Symbols for Diagrams — Binary Logic Elements