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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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