Digital Logic Toolkit

Digital Logic Toolkit — NOT gate

Source
https://digitallogictoolkit.com/not-gate/
Printed

Double inversion: (A′)′ — NOT gate

coretwo inverters cancel

Answer

verified equivalent (both sides → A)

Why this example is worth doing

Two inverters in series restore the original signal, which is involution and looks like a waste of two gates. It is not: a pair of inverters is a standard buffer used to restore signal edges and drive a heavy load, so the logically redundant circuit is electrically essential. The page uses this to draw the line between logical function and physical implementation clearly, a distinction the buffer page then develops.

Try your own input in the NOT gate. Truth table, symbol and algebraic form for the inverter, Ā.

How the answer is reached

The law

A′′A— Both sides have the same truth table over the union of their variables.

Truth table

Truth table — columns #, A, F
#AF
000
111

Compare with

Open the NOT 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