NOR as an inverted-input AND — NOR gate

edge casethe alternative symbol

Answer

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

Why this example is worth doing

The De Morgan equivalent: an AND body with both inputs bubbled. In a NOR-only design these alternate with the plain NOR symbol so that bubbles pair off along each path, making the underlying OR-AND structure legible. The page shows the same three-gate network drawn both ways — all plain NOR symbols, then with alternating symbols — and the second is dramatically easier to read. That comparison is the argument for bothering with two symbols per gate.

Try your own input in the NOR gate. Truth table, symbol and algebraic form for (A + B)′, the other universal gate.

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 NOR 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