IT25 BOOLEAN FUNCTIONS
Boolean Functions - Computer Organization (IT 25)
BOOLEAN FUNCTIONS
A Boolean function consists of a binary variable denoting the function, an equals sign and an algebraic expressions formed by using binary variables the constants
0 and 1, the logic operation symbols, and parentheses. For a given value of the binary variables, Boolean function can be equal to either 1 or 0.
Example:
F = X + Y’Z
The two parts of the expression X and Y’Z, are called terms of the function F.
The function F is equal to 1 if term X is equal to 1 or if term Y’Z are equal to 1.
Otherwise, F is equal to 0. A Boolean function expresses the logical relationship between binary variables. It is evaluated by determining the binary value of the expression for all possible combinations of values for the variables.
A Boolean function can be represented in truth table and can be transformed into a circuit diagram composed of logic gates.
Truth table of:
X
0
0
0
0
1
1
1
1
Y
0
0
1
1
0
0
1
1
F = X + Y’Z
Z
0
1
0
1
0
1
0
1
F
0
1
0
0
1
1
1
1
Logic Circuit diagram
X
Y
F
Z
By: E. Omictin
Boolean Functions - Computer Organization (IT 25)
Standard Forms
The standard forms of a Boolean expression contains product terms and sum terms. An example of a product term is XY’Z. This is logical product consisting of an AND operation among three literals. An example of a sum term is X+Y+Z’.
This is a logical sum consisting of an OR operation among the literals.
Minterms and Maxterms
An algebraic expression representing a Boolean function is derived from a truth table by finding the logical sum of all product terms for which the function assumes the binary value 1.
A product term in which all variables appear exactly once, either complemented or uncomplemented, is called a minterm. It is possible to formulate 2n minterms with n variables. Each minterm is a product term of exactly n literals.
Minterms for Three variables
X
BOOLEAN FUNCTIONS
A Boolean function consists of a binary variable denoting the function, an equals sign and an algebraic expressions formed by using binary variables the constants
0 and 1, the logic operation symbols, and parentheses. For a given value of the binary variables, Boolean function can be equal to either 1 or 0.
Example:
F = X + Y’Z
The two parts of the expression X and Y’Z, are called terms of the function F.
The function F is equal to 1 if term X is equal to 1 or if term Y’Z are equal to 1.
Otherwise, F is equal to 0. A Boolean function expresses the logical relationship between binary variables. It is evaluated by determining the binary value of the expression for all possible combinations of values for the variables.
A Boolean function can be represented in truth table and can be transformed into a circuit diagram composed of logic gates.
Truth table of:
X
0
0
0
0
1
1
1
1
Y
0
0
1
1
0
0
1
1
F = X + Y’Z
Z
0
1
0
1
0
1
0
1
F
0
1
0
0
1
1
1
1
Logic Circuit diagram
X
Y
F
Z
By: E. Omictin
Boolean Functions - Computer Organization (IT 25)
Standard Forms
The standard forms of a Boolean expression contains product terms and sum terms. An example of a product term is XY’Z. This is logical product consisting of an AND operation among three literals. An example of a sum term is X+Y+Z’.
This is a logical sum consisting of an OR operation among the literals.
Minterms and Maxterms
An algebraic expression representing a Boolean function is derived from a truth table by finding the logical sum of all product terms for which the function assumes the binary value 1.
A product term in which all variables appear exactly once, either complemented or uncomplemented, is called a minterm. It is possible to formulate 2n minterms with n variables. Each minterm is a product term of exactly n literals.
Minterms for Three variables
X