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Logic Systems

Updated : August 14, 2019

Two-valued Logic (2-VL)

It is the most commonly used logic system.

There are Logical Constants : False and True (which are often expressed as 0 and 1)

There are 16 Logical Functions including AND, OR, NOT, XOR.

Boolean Algebra is named after George Boole (Cambridge), author of “Laws of Thought”

Switching Circuit Theory : Claude Shanon (MIT) proposed the use of logic in the design and implementation of switching circuits.

Early digital computers have ALU (Arithmetic Logic Unit).

Most Programming Languages support Logical Operators.

Three Valued Logic (3-VL)

Sample use : Yes, No, DNK (Do Not Know)

There are three Logical Constants : 0, 1, 2

The Logical Operators are defined by truth tables.

For two logic variables, there are 9 possible combinations
(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)

Example : MAX (for Maximum)
MIN (for Minimum)

Fuzzy Set

Zadeh (Stanford) proposed fuzziness as a “degree of membership in a set”.

Applications of Fuzzy Set are found in appliances such as Washers and Dryers.

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