Discrete Math Notes:
Chapter 8: Applications of Discrete Mathematics
8.1 An introduction to Boolean algebra
Boolean algebra, a set of rules and operations for working with variables whose values are either 0 or 1
Boolean multiplication, applies to two elements from {0, 1} and obeys the standard rules for multiplication.
Boolean addition, applies to two elements from {0, 1} and obeys the standard rules for addition, except for 1 + 1.
Complement, an element, denoted with a bar symbol, reverses that element's value
digital logic, the area of computer science concerned with designing computer circuitry
Boolean variables,variables that can have a value of 1 or o
Boolean expressions, can be built up by applying Boolean operations to Boolean variables or the constants 1 or 0.
Equivalent, Two Boolean expressions are equivalent if they have the same value for every possible combination of values assigned to the variables contained in the expressions.
Overview:
Boolean algebra is a collection of rules and operations for dealing with variables that have either a 0 or a 1 value. If you've studied propositional logic, you'll recognize the rules for Boolean algebra. In reality, Boolean operations definitions are just a restatement of logical operations with somewhat different syntax. - denotes Boolean multiplication, which applies to two elements from 0 to 1 and follows the standard multiplication rules. - denotes Boolean multiplication, which applies to two elements from 0 to 1 and follows the standard multiplication rules. Except for 1 + 1, Boolean addition, indicated by +, applies to two elements from 0 to 1 and follows the conventional rules for addition. Because all values in Boolean algebra must be 0 or 1, a result of ff would be unacceptable. The value of an element's complement, represented by a bar sign, is reversed. The importance of logic in this discipline is demonstrated by the use of digital logic. Boolean variables are variables that can have a value of 1 or 0. Applying Boolean operations to Boolean variables or the constants 1 and 0 can be used to create Boolean expressions