The distributive law is the factoring law. A + (B +C) = (A + B) + C For multiplication, the associative law states When ANDing more than two variables, the result is the same regardless of the grouping of the variables. For addition, the associative law states When ORing more than two variables, the result is the same regardless of the grouping of the variables. The associative laws are also applied to addition and multiplication. A + B = B + A For multiplication, the commutative law states In terms of the result, the order in which variables are ANDed makes no difference. For addition, the commutative law states In terms of the result, the order in which variables are ORed makes no difference. The commutative laws are applied to addition and multiplication. What are the values of the A, B and C if the product term of A.B.C = 1? Example Solution Each literal must = 1 therefore A = 1, B = 0 and C = 0. The product term will be 1 only if all of the literals are 1. The product of literals forms a product term. In Boolean algebra, multiplication is equivalent to the AND operation. Determine the values of A, B, and C that make the sum term of the expression A + B + C = 0? Example Solution Each literal must = 0 therefore A = 1, B = 0 and C = 1.ģ Summary Example Solution Boolean Multiplication The sum term is zero only if each literal is 0. The sum term is 1 if one or more if the literals are 1.
Addition is equivalent to the OR operation. A literal is a variable or its complement. The complement represents the inverse of a variable and is indicated with an overbar. A single variable can only have a value of 1 or 0. In Boolean algebra, a variable is a symbol used to represent an action, a condition, or data. 1 Digital Fundamentals Floyd Chapter 4 Tenth EditionĢ Summary Example Solution Boolean Addition
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