NOR — and its inverted-input AND equivalent — logic gate symbols

coreDe Morgan drawn twice

Answer

verified equivalent (both sides → A′ · B′)

Why this example is worth doing

The same physical NOR gate has two legal symbols: an OR body with an output bubble, and an AND body with bubbles on both inputs. They are De Morgan's law in picture form, and both appear in real schematics — designers choose whichever makes the bubbles cancel against the neighbouring gates. The page presents them as alternates rather than as a puzzle, because a student meeting the inverted-input form for the first time in someone else's drawing usually assumes it is a different part.

Try your own input in the Logic gate symbols. Every gate in both symbol standards, side by side, on a printable one-page chart.

How the answer is reached

The law

(A + B)′A′ · B′Both sides have the same truth table over the union of their variables.

Truth table

Truth table — columns #, A, B, F
#ABF
0001
1010
2100
3110

Compare with

Open the Logic gate symbols

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