Digital Logic Toolkit

Digital Logic Toolkit — NAND gate

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

A = 1, B = 1 — NAND gate

introthe only false row

Answer

output 0

Why this example is worth doing

Both inputs high is the one combination that drives a NAND low, which is the fastest way to hold the gate in mind: NAND is false only when everything is true. The page opens on that row because it is the complement of the AND row a student has usually just read, and the two pages are deliberately structured so that flipping between them shows one inverted column.

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

The probed row

A = 1, B = 10— Row 3 of 4.

Truth table

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

Compare with

Open this example in the NAND gate

The field arrives filled in with this example’s input.

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)