Tugas 7.Aljabar Boolean, Penyederhanaan Logika dan Peta Karnaugh

Aljabar Boolean, Penyederhanaan Logika dan Peta Karnaugh

Standard Forms of Boolean Expressions

·         Sum of Product (SOP)

·         Product of Sum (POS)

The Sum-of-Products (SOP) Form

When two or more product terms are summed by Boolean addition

Conversion of a General Expression to SOP Form

Any logic expression can be change into SOP form by applying Boolean Algebra techniques

The Standard SOP Form

The Products-of-Sum (POS) Form

When two or more sum terms are multiplied.

The Standard POS Form

Boolean Expression and Truth Table

Converting SOP to Truth Table

Boolean Expression and Truth Table

§  Examine each of the products to determine where the product is equal to a 1.

§   Set the remaining row outputs to 0.

Converting POS to Truth Table

    §  Opposite process from the SOP expressions.

    §  Each sum term results in a 0.

    §  Set the remaining row outputs to 1.

Converting from Truth Table to SOP and POS

The Karnaugh Map

The Karnaugh Map

 ·  Provides a systematic method for simplifying Boolean expressions

 · Produces the simplest SOP or POS expression

· Similar to a truth table because it presents all of the possible values of input variables.

The 3-Variable K-Map

The 4-Variable K-Map

K-Map SOP Minimization

§  A 1 is placed on the K- Map for each product term in the expression.

§  Each 1 is placed in a cell corresponding to the value of a product term.

Example:

Map the following standard SOP expression on a K-Map:

Example: Map the following standard SOP expression on a K-Map :

Exercise:

Map the following standard SOP expression on a K-Map:

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