Aljabar Boolean, Penyederhanaan Logika dan Peta Karnaugh
Standart form of Boolean expressions
Ø Sum
of Product (SOP)
Ø Product
of Sum (POS)
(SOP form) when two or more product term are summed by
Boolean addition.
Conversion of a general expression to SOP form
The standard SOP form
The product -of-sum (POS) form
Boolean Expression and Truth Table
Converting SOP to Truth Table
· Examine
each of the products to determine where the product is equal to a 1
· Set
the remaining row uotputs to 0
Conveting POS to Truth Table
· Opposite
process form the SOP Expression.
· Each
sum term result in a 0
· Set
the remaining roe outputs to 1
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
K-Map simplication of SOP Expression
· A
group must contain either 1, 2, 4, 8 or 16 cells.
· Each
cell in group must be adjacent to one or more cells in that same group but all
cells in the group do not have to be adjacent to each other
· Always
include the largest possible number 1s in a group in accordance with rule 1
·
Each 1 on the map must be included in at
least one group. The 1s already in a group can be included in another group as
long as the overlapping groups include noncommon 1s.
Groups the cells that have 1s. Each group of cells containing 1s create one product term composed of all variables that occur in only one form (either uncomplemented or complemented) within the group. Variable that occurs both uncomplemented and complemented within the group are eliminated. These are called contradictory variables.
sumber : https://www.kabarmutiongkok.org/uhamka/category/06-chapter-06
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