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Boolean Expressions
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Terms in this set (49)
Sum of Products (minterm)
Product of Sum( max term)
Demorgans Theorems
0 +0 =
0
0+1 =
1
1+0 =
1
1+1 =
1
0*0 =
0
0*1 =
0
1*0 =
0
1*1 =
1
A+B =
B+A
AB =
BA
A+(B+C) =
(A+B)+C
A(BC) =
(AB)C
Associative Law of Multiplication:
MAKES NO DIFFERENCE IN WHAT ORDER VARIABLES ARE GROUPED WHEN ANDinG MORE THEN TWO VARIABELS.
Associative Law of Addition:
ORING MORE THEN TWO VARIABLES, THE RESULT IS THE SAME REGARDLESS OF THE GROUPING OF THE VARIABLES
Commutative Law of addition:
THE ORDER IN WHICH THE VARIABLES ARE ORED MAKES NO DIFFERENCE
Commutative Law of Multiplication States:
THE ORDER IN WHCIH THE VARIABLES ARE ANDED MAKES N0 DIFFERENCE.
Distributive Law States:
THAT ORING TWO OR MORE VARIABLES AND THEN ANDING THE RESULTS WITH A SINGLE VARIABLE IS EQUIVALENT TO ANDing THE SINGLE VARIABLE WITH EACH OF THE TWO OR MORE VARIABLES AND THEN ORing the PRODUCTS
A(B+C) =
AB +AC
A*A =
A
A+0 =
A
A+1 =
1
A*0 =
0
A*1 =
A
A+A =
A
A+A' =
1
A*A' =
0
A'' =
A
A+ AB =
A
A+A'B =
A+B
(A+B)(A+C) =
A+BC
DEMORGANS FIRST THEOREM
THE COMPLEMENT OF A PRODUCT OF VARIABLES IS EQUAL TO THE SUM OF THE COMPLEMENTS OF THE VARIABLES
THE COMPLEMENT OF TWO OR MORE ANDed VARIABLES IS EQUIVALENT TO THE OR OF THE COMPLEMENTS OF THE INDIVIDUAL VARIABLES
DEMORGANS THEOREM
DEMORGANS SECOIND THEROEM
The complement of a sum of variables is equal to the product of the complements of the variables
The complement of two or more variables ORed variables is equivalent to the AND of the complements of the individual variables.
DeMorgans Second theorem.
When two or more products terms are summed by Boolean addition the resulting expression is a:
sum-of-products
Domain of a Boolean Expression
The set of variables contained in the expression in either complemented or uncomplemented form.
Product-of-Sums
When two or more sum terms are multiplied, the resulting expression is a product-of-sums.
(A+B)'=Y
A'*B'=Y
(A*B)'=Y
A'+B'=Y
STEP 1 FOR CONVERTING MINS-TO-MAX
Change all Or's to AND's and all AND's to OR's
STEP 2: CONVERTING MINS-TO-MAX
Complement each individual variable (add short overbars to each)
STEP 3 : CONVERTING MINS-TO-MAX
Complement the entire function (Add long overbar to entire function)
STEP 4: CONVERTING MINS -TO-MAX
Eliminate all groups of Double overbars.
Difference Between SOP AND POS
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