Digital Logic Toolkit

Digital Logic Toolkit — XNOR gate

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

A ⊙ 0 and A ⊙ 1 — XNOR gate

corethe mirror of the XOR identity

Answer

A ⊙ 0 column 10, A ⊙ 1 column 01

Why this example is worth doing

XNOR against a constant behaves exactly opposite to XOR against a constant, so a design needing a controlled inverter can use either gate with the control polarity flipped. The page tabulates all four combinations on one line and notes that this is why active-low control signals and XNOR gates so often appear together — the polarity inversion is absorbed into the gate rather than costing an inverter.

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

Output table

Output table — columns A, A ⊙ 0, A ⊙ 1
AA ⊙ 0A ⊙ 1
010
101

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