Digital Logic Toolkit

Digital Logic Toolkit — XNOR gate

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

Full 2-input truth table — XNOR gate

introtrue when the inputs agree

Answer

output column 1001

Why this example is worth doing

The XOR column inverted, and the same table as the biconditional from propositional logic. The page prints the logic-course notation A ↔ B and the engineering notation A ⊙ B in the same header, because this gate has two entirely separate audiences arriving with different vocabularies for one object. Making that explicit is worth more than either notation alone.

Try your own input in the XNOR gate. Truth table, symbol and algebraic form for A ⊙ B, the equality detector.

How the answer is reached

Truth table

Truth table — columns #, A, B, A ⊙ B
#ABA ⊙ B
0001
1010
2100
3111

Compare with

Open the XNOR 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