Saturday, January 4, 2014

Boolean Algebra & Logic Gates for A/L ICT










Boolean algebra or Boolean logic is a calculation of truth values, developed by George Boole in the 1840s. In ICT it resembles logical multiplication xy, addition x + y, and negation −x to build combined circuits.

Boolean logic or Boolean algebra is a logical calculus which has only two values, 'true' or 'false'.
Boolean Logic is defined as a logical system of operators - 'AND', 'OR' and 'NOT'. It is a way of comparing individual bits and used in computer construction, switching circuits, etc.

' denotes negative
Boolean Algebra Quiz




1. Give the relationship that represents the dual of the Boolean property A + 1 = 1?
(Note: * = AND, + = OR and ' = NOT)
1. A * 1 = 1
2. A * 0 = 0
3. A + 0 = 0
4. A * A = A
5. A * 1 = 1

2. Give the best definition of a literal?
1. A Boolean variable
2. The complement of a Boolean variable
3. 1 or 2
4. A Boolean variable interpreted literally
5. The actual understanding of a Boolean variable

3. Simplify the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) and choose the best answer.
1. A + B + C
2. D + E
3. A'B'C'
4. D'E'
5. None of the above

4.Which of the following relationships represents the dual of the Boolean property x + x'y = x + y?
1. x'(x + y') = x'y'
2. x(x'y) = xy
3. x*x' + y = xy
4. x'(xy') = x'y'
5. x(x' + y) = xy

5.Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent most simplified Boolean representation for F is:
1. Z + YZ
2. Z + XYZ
3. XZ
4. X + YZ
5. None of the above

6. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
1. A + B
2. A'B'
3. C + D + E
4. C'D'E'
5. A'B'C'D'E'

7. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?
1. F'= A+B+C+D+E
2. F'= ABCDE
3. F'= AB(C+D+E)
4. F'= AB+C'+D'+E'
5. F'= (A+B)CDE

8. An equivalent representation for the Boolean expression A' + 1 is
1. A
2. A'
3. 1
4. 0

9. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
1. ABCDEF
2. AB
3. AB + CD + EF
4. A + B + C + D + E + F
5. A + B(C+D(E+F))

Answers
1. A * 0 = 0. The dual of any Boolean property may be obtained by interchanging all occurrences of the symbols (*,+,0,1) with the symbols (+,*,1,0). Beware of implicit AND operations (like xy); these ANDs are also converted to +. Therefore, the dual of x + 1 = 1 is: x*0 = 0.

2. 1 or 2
3. A + B + C
4. x(x' + y) = xy
5. Z + XYZ

6. A'B'
7. (A+B)CDE (DeMorgan's theorem twice)
8. 1
9. AB

OSI (Open Systems Interconnect) Model Animation

The Open Systems Interconnection model (OSI model) introduced by International Organization for Standardization. It standardizes the functions of a communications system in terms of layers. OSI groups similar communication functions into logical layers. An instance of a layer provides services to its upper layer instances while receiving services from the layer below.

For example, a layer that provides error-free communications across a network provides the path needed by applications above it, while it calls the next lower layer to send and receive packets that make up the contents of that path.










Layer 1: Physical layer 
defines electrical and physical specifications for devices.
defines the relationship between a device and a transmission medium, such as a copper or optical cable, including the layout of pins, voltages, cable specifications, hubs, repeaters, network adapters and more.

Establishment and termination of a connection to a communications medium.
Sharing communication resources effectively among multiple users.
Modulation (conversion from and to digital)

Layer 2: data link layer
Provides the functional and procedural means to transfer data between network entities and to detect and possibly correct errors that may occur in the physical layer.

IEEE 802.3 dominant wired LAN protocol (ETHERNET)
IEEE 802.11 the wireless LAN protocol

Layer 3: network layer
Provides the functional and procedural means of transferring variable length data sequences from a source host on one network to a destination host on a different network.
Performs network routing functions, and might also perform fragmentation and reassembly, and report delivery errors. Routers operate at this layer, sending data throughout the extended network and making the Internet possible.

Layer 4: transport layer
Provides transparent transfer of data between end users, providing reliable data transfer services to the upper layers. The transport layer controls the reliability of a given link through flow control, segmentation/desegmentation, and error control. Some protocols are state- and connection-oriented. This means that the transport layer can keep track of the segments and retransmit those that fail. The transport layer also provides the acknowledgement of the successful data transmission and sends the next data if no errors occurred.

Transport layer is like a Post Office, which deals with the dispatch and classification of mail and parcels sent. The post office manages the outer envelope of mail. Higher layers may have the equivalent of double envelopes, such as cryptographic presentation services that can be read by the addressee only.

The Transmission Control Protocol (TCP) and the User Datagram Protocol (UDP) of the Internet Protocol Suite are commonly categorized as layer-4 protocols within OSI.

Layer 5: session layer
Controls the dialogues (connections) between computers. It establishes, manages and terminates the connections between the local and remote application. It provides for full-duplex, half-duplex, or simplex operation, and establishes checkpointing, adjournment, termination, and restart procedures. The OSI model made this layer responsible for graceful close of sessions, which is a property of the Transmission Control Protocol, and also for session checkpointing and recovery, which is not usually used in the Internet Protocol Suite. The session layer is commonly implemented explicitly in application environments that use remote procedure calls.

Layer 6: presentation layer
Establishes context between application-layer entities, providing independence from data representation (e.g., encryption) by translating between application and network formats. The presentation layer transforms data into the form that the application accepts.

Converting an EBCDIC-coded text file to an ASCII-coded file, or serialization of objects and other data structures from and to XML.

Layer 7: application layer
The application layer is the OSI layer closest to the end user, which means that both the OSI application layer and the user interact directly with the software application. Application-layer functions typically include identifying communication partners, determining resource availability, and synchronizing communication. Synchronizes communication between applications requires cooperation that is managed by the application layer.

Some examples on TCP/IP stack: 
  • Hypertext Transfer Protocol (HTTP),
  • File Transfer Protocol (FTP),
  • Simple Mail Transfer Protocol (SMTP)
  • Simple Network Management Protocol (SNMP).