In addition to floppy disks and hard drives, today's computer user can choose from a wide range of storage devices, from “key ring" devices that store hundreds of megabytes to digital video discs, which make it easy to transfer several gigabytes of data. This lesson examines the primary types of storage found in today's personal computers. You'll learn how each type of storage device stores and manages data. | Boolean Algebra Chapter 12 Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Summary Boolean Functions Representing Boolean Functions Logic Gates Minimization of Circuits (not currently included in overheads) Claude Shannon (1916 - 2001) Boolean Functions Section Section Summary Introduction to Boolean Algebra Boolean Expressions and Boolean Functions Identities of Boolean Algebra Duality The Abstract Definition of a Boolean Algebra Introduction to Boolean Algebra Boolean algebra has rules for working with elements from the set {0, 1} together with the operators + (Boolean sum), (Boolean product), and . These operators are defined by: Boolean sum: 1 + 1 = 1, 1 + 0 = 1, 0 + 1 = 1, 0 + 0 = 0 Boolean product: 1 1 = 1, 1 0 = 0, 0 1 = 0, 0 0 = 0 complement: = 1, = 0 Example: Find the value of 1 0 + Solution : 1 0 + = 0 + = 0 + 0 = 0 Boolean Expressions and Boolean Functions Definition: Let B = {0, 1}. Then Bn = {(x1, x2, , xn) | xi ∈ B for 1 ≤ i ≤ n } is the set of all possible n-tuples of 0s and 1s. The variable x is called a Boolean variable if it assumes values only from B, that is, if its only possible values are 0 and 1. A function from Bn to B is called a Boolean function of degree n. Example: The function F(x, y) = x from the set of ordered pairs of Boolean variables to the set {0, 1} is a Boolean function of degree 2. Boolean Expressions and Boolean Functions (continued) Example: Find the values of the Boolean function represented by F(x, y, z) = xy + . Solution: We use a table with a row for each combination of values of x, y, and z to compute the values of F(x,y,z). Boolean Expressions and Boolean Functions (continued) Definition: Boolean functions F and G of n variables are equal if and only if F(b1, b2, , bn)= G(b1, b2, , bn) whenever b1, b2, , bn belong to B. Two different Boolean expressions that represent the same function are . | Boolean Algebra Chapter 12 Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Summary Boolean Functions Representing Boolean Functions Logic Gates Minimization of Circuits (not currently included in overheads) Claude Shannon (1916 - 2001) Boolean Functions Section Section Summary Introduction to Boolean Algebra Boolean Expressions and Boolean Functions Identities of Boolean Algebra Duality The Abstract Definition of a Boolean Algebra Introduction to Boolean Algebra Boolean algebra has rules for working with elements from the set {0, 1} together with the operators + (Boolean sum), (Boolean product), and . These operators are defined by: Boolean sum: 1 + 1 = 1, 1 + 0 = 1, 0 + 1 = 1, 0 + 0 = 0 Boolean product: 1 1 = 1, 1 0 = 0, 0 1 = 0, 0 0 = 0 complement: = 1, = 0 Example: Find the value of 1 0 + Solution : 1 0 + = 0 + = 0 + 0 = 0 Boolean Expressions and Boolean .
