OR from NOR gates only — OR gate

exam standarduniversal-gate construction

Answer

2 NOR gates realising B + A

Why this example is worth doing

The NOR-only construction of OR mirrors the NAND-only construction of AND exactly: compute the inverted function, then invert it back with a second gate whose inputs are tied. Presenting the two side by side is the clearest way to show that NAND-world and NOR-world are the same world under duality, and that anything provable in one has a mechanical translation into the other. The universal gates page takes this up systematically.

Try your own input in the OR gate. Truth table, symbol and algebraic form for A + B, with a live two-input toggle.

How the answer is reached

Gate list

Gate list — columns Node, Gate, Inputs
NodeGateInputs
g1norA, B
g2norg1, g1

NOR-only realisation

A ↓ B ↓ (A ↓ B)B + A2 NOR gates, verified by reading the network back out.

Truth table

Truth table — columns #, A, B, A ↓ B ↓ (A ↓ B)
#ABA ↓ B ↓ (A ↓ B)
0000
1011
2101
3111

Compare with

Open the OR 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