Boolean Theory
• Boolean theory provides the fundamentals for logic operators and operation to
perform Boolean algebra.
• Boolean algebra is a branch of mathematics that includes methods for manipulating
logical variables and logical expressions.
• The Greek philosopher Aristotle founded a system of logic based on only two types
of propositions: true and false.
• The English mathematician George Boole (1815–1864) sought to give symbolic form
to Aristotle’s system of logic—hence the name Boolean algebra.
• In the mid-twentieth century, Claude Shannon, an electrical engineer and
mathematician, applied Boole’s ideas to digital circuits.
,Logic Variables and Logic Functions
• Like algebra, Boolean algebra is based on a set of rules that are derived from a small
number of basic assumptions. Logic values involve elements that take on one of two
values, 0 and 1. Therefore, a logic variable can only be equal to 0 or 1.
• A logic function is an expression, that describes the logic operations between its logic
variables. Similarly, a logic function can only be equal to 0 or 1.
,BOOLEAN AXIOMS AND THEOREMS
• The basic logic operations include logic sum (+), logic product (·), and logic
complement (‘). i.e. OR, AND and NOT
• If a logic variable is true, its logic complement is false.
• In 1904 Huntington defined 6 postulates that must be satisfied, called Huntington’s
postulates
,
• Boolean theory provides the fundamentals for logic operators and operation to
perform Boolean algebra.
• Boolean algebra is a branch of mathematics that includes methods for manipulating
logical variables and logical expressions.
• The Greek philosopher Aristotle founded a system of logic based on only two types
of propositions: true and false.
• The English mathematician George Boole (1815–1864) sought to give symbolic form
to Aristotle’s system of logic—hence the name Boolean algebra.
• In the mid-twentieth century, Claude Shannon, an electrical engineer and
mathematician, applied Boole’s ideas to digital circuits.
,Logic Variables and Logic Functions
• Like algebra, Boolean algebra is based on a set of rules that are derived from a small
number of basic assumptions. Logic values involve elements that take on one of two
values, 0 and 1. Therefore, a logic variable can only be equal to 0 or 1.
• A logic function is an expression, that describes the logic operations between its logic
variables. Similarly, a logic function can only be equal to 0 or 1.
,BOOLEAN AXIOMS AND THEOREMS
• The basic logic operations include logic sum (+), logic product (·), and logic
complement (‘). i.e. OR, AND and NOT
• If a logic variable is true, its logic complement is false.
• In 1904 Huntington defined 6 postulates that must be satisfied, called Huntington’s
postulates
,
