Four-valued logic

Four-Valued Logic

Four-valued logic

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Description:
In logic, a four-valued logic is used to model signal values in digital circuits: the four values are Z, X and the boolean values 1 and 0. Z stands for high impedance or open circuit, while X stands for "unknown". There is also a 9-valued logic standard by the IEEE called IEEE 1164.

There are other types of four value logic, such as Belnap's four-valued relevance logic: the possible values are 1) true, 2) false, 3) both true and false, and 4) neither true nor false. Belnap's logic is designed to cope with multiple information sources such that if only true is found then true is assigned, if only false is found then false is assigned, if some sources say true and others say false then both is assigned, and if no information is given by any information source then neither is assigned.

Applications

Electronics

Digital electronics theory supports four distinct logic values (as defined in VHDL's std_logic):
  • 1 or High, usually representing TRUE.
  • 0 or Low, usually representing FALSE.
  • X representing a "Conflict".
  • U representing "Unassigned" or "Unknown".
  • - representing "Don't Care".
  • Z representing "high impedance", undriven line.
  • H, L and W are other high-impedance values, the weak pull to "High", "Low" and "Don't Know" correspondingly.


The "X" value does not exist in real-world circuits, it is merely a placeholder used in simulators and for design purposes. Some...
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