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Boolean Expression and Logic Circuit

Boolean Expression

Axioms of Boolean Algebra
Basic Theorems
Logical Addition (OR operation)
Logical Multiplication (AND operation)
Complementation

Logic Gate

an electronic circuit operates on one or more input signals to produce an output signal
gates are digital signal (two-state) circuits
can be analyzed with Boolean Algebra
OR gate : circuit which performs OR operation
AND gate : circuit which performs AND operation

Electrical Switches

closed / ON = 1
open / OFF = 0

Boolean Algebra

basic rules for simplifying and combining logic gates
has either two values : true / false (1 or 0)
two types of operator : (i) Unary (NOT) (ii)Binary (AND , OR)
eg : Y = A . B @ Y = AB @ Y = A+B @ Y = A'

Universal gates :

- gate that can have two or more inputs

NAND : its output is true if NOT all inputs are true
NOR : its output is true if no inputs are true

Truth Table

way to show the function of a logic gate
shows the output states
the symbols 0 (false) and 1 (true) are used in truth table
example of truth table :

Information Coding Schemes

Information Coding Schemes ~

The combination of 0 and 1 that represent characters are defines by pattern called a Coding scheme.

Popular Coding scheme :

ASCI/Extended ASCI (America Standard Code for Information Interchange)

- Use 8 bits to represent a character
- Can represent 256 character (2 to the power of 8 = 256)
- Used on PC and server

EBCDIC (Extended Binary Coded Decimal Interchange Code)

- Use 8 bits to represent a character
- Can represent 256 character (2 to the power of 8 = 256)
- Used on IBM mainframe and high end servers

Unicode (Uniform code capable of representing all world's languages)

- Used 16 bits to represent a character
- Can represent >65000 characters (2 to the power of 16 = 65000)
- Implemented in several OS (Windows, Mac OS, Linux)

^__^ TQ

How Does A Computer Represent Data?
.....by using two unique binary digit 1 and 0to represent thetwo states of on and off.
......a computer circuit represents the 0 or the 1 electronically by the presence or absence of an electrical charge

*computer recognizes only two discrete electrical states (on and off)

BIT -is the smallest unit of data the computer can process ( BINARY DIGIT )
-the number of the system has two unique digit, 1(ON) or 0(OFF)
-represents an electrical state (on or off)

BYTE-a group of 8 bits
-represents a single character such as a digit, a letter, a punctuation mark, or any symbol in computer.

ASCII(American Standard Code for Information Interchange) is the most widely used coding scheme to represent data

Storage

Storage

❥ Storage holds data , instructions and information for future use
❥ A storage medium /,media is the physical material on which a computer keeps data , instructions and information .

Storage Capacity

♬ Capacity is the number of bytes a storage medium can hold

Kilobytes = 1,024 bytes
Megabytes = 1,024 Kilobytes
Gigabytes = 1,024 Megabytes
Terabytes = 1,024 Gigabytes

Conversion unit

1 GB = 1 x 1024 x 1024 OR 1 GB = 1 X 2^10 X 2 ^10

= 1 048 576 KB =1 048 576 KB

1200 MB = 1200 / 1024 OR 1200 MB = 1200 / 2^10

= 1.17 GB = 1.17 GB

STORAGE DEVICE

A storage is the computer hardware that records and retrieves items to and from storage media .
To store data and programs when they are not being processed .
Stores files permanently.
Available in the form of hard disk, CD, USB drive etc

Types of Storage

• Magnetic Storage

• Optical Storage

• Flash memory

Magnetic Storage

– Uses different patterns of magnetization on a magnetically coated surface to store information.

– Examples of magnetic storage are:

❤ Hard Disk

❤ Floppy disk

ლ Hard Disk

A hard disk contains one or more inflexible,circular platters that use magnetic particles to store data, instructions, and information

Optical Discs Storage

❣ Stores information in deformities on the surface of a circular disc and reads this information by illuminating the surface with a laser diode and observing the reflection.

❣ Types of optical disc are:

» Compact Disc (CD)

» Digital Video Disc (DVD)

» Blu-ray Disc (BD)