Digital Logic Toolkit

Digital Logic Toolkit — NAND gate

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

Full 2-input truth table — NAND gate

intro3 of 4 rows true

Answer

output column 1110

Why this example is worth doing

The AND column inverted, and the table behind the largest single block of search demand on the gate pages. The page presents it with the AND column beside it rather than alone, because the relationship is the content: NAND is not a new function to memorise but a derived one, and every property it has follows from AND plus an inversion.

Try your own input in the NAND gate. Truth table, symbol and algebraic form for (A·B)′, the universal gate.

How the answer is reached

Truth table

Truth table — columns #, A, B, A ↑ B
#ABA ↑ B
0001
1011
2101
3110

Compare with

Open the NAND 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
  • Sheffer, “A Set of Five Independent Postulates for Boolean Algebras” (1913)