Binary Numbering Systems and Character Representation in Computing
CMIT100
CHAPTER 3 - BINARY NUMBERING SYSTEM
Learning Objectives
Describe Numbering Systems: decimal, binary, octal, and hexadecimal.
Describe how characters are stored in computer memory.
Demonstrate the application of binary (Boolean) operations of AND, OR, NOT, and XOR on binary
numbers.
Illustrate the use of binary in a computer with a focus on IP addresses.
Numbering Systems
Decimal – Base 10
Binary – Base 2
Octal – Base 8
Hexadecimal – Base 16
Base 10 System - Decimal
Primary human numbering system
Digits 0 – 9
Example: 1, 2, 10, 4,321
Base 2 System - Binary
Native numbering system for digital computers
Two digits: 0, 1
Each digit is a bit that represents on or off
Eight bits is a byte; also known as an octet
Example: 0, 1, 10, 101, 1100
Base 8 - Octal
Digits 0 – 7
Examples: 1, 5, 112
Base 16 - Hexadecimal
Digits 0 – F
Examples: 0, 1, 3FA7
Converting between Decimal and Binary
Character Representation
American Standard Code for Information Interchange (ASCII)
Unicode – An extension of ASCII
EBCDIC - Discontinued
ASCII
•
7-bit
•
128 combinations
Extended ASCII
•
8-bit
•
256 combinations
Unicode
Extended ASCII is not enough for international use
One Unicode mapping uses 16 bits per character
65363 Combinations
Unicode is a superset of ASCII
◦
The first 256 characters correspond exactly to the extended ASCII character set
Unicode Table (Example)
Binary Operations
NOT
AND
OR
NAND
NOR
XOR
Gate - A device that performs a basic operation on electrical signals
Circuit - Gates combined to perform more complicated tasks
Binary Operations – NOT
A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output
Binary Operations – AND
An AND gate accepts two input signals
◦
If both are 1, the output is 1; otherwise, the output is 0
Binary Operations – OR
An OR gate accepts two input signals
◦
If both are 0, the output is 0; otherwise, the output is 1
Binary Operations – NAND
The NAND gate accepts two input signals
If both are 1, the output is 0; otherwise, the output is 1
Binary Operations – NOR
The NOR gate accepts two input signals
If both are 0, the output is 1; otherwise, the output is 0
Binary Operations – XOR
An XOR gate accepts two input signals
If both are the same, the output is 0; otherwise, the output is 1
Review of Gate Processing
A NOT gate inverts its single input
An AND gate produces 1 if both input values are 1
An OR gate produces 0 if both input values are 0
An XOR gate produces 0 if input values are the same
A NAND gate produces 0 if both inputs are 1
A NOR gate produces a 1 if both inputs are 0
Constructing Gates
A transistor has three terminals
◦
A source
◦
A base
◦
An emitter, typically connected to a ground wire
Constructing Gates
The easiest gates to create are the NOT, NAND, and NOR gates
Combinational Circuits
Gates are combined into circuits by using the output of one gate as the input for another
Integrated Circuits
Creative Commons Statement
Explore the world of numbering systems including decimal, binary, octal, and hexadecimal, and delve into how characters are stored in computer memory. Learn about Boolean operations and their application on binary numbers, with a focus on IP addresses. Discover the importance of ASCII, Unicode, and the transition to 16-bit characters for international use.
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Presentation Transcript
CMIT100 CHAPTER 3 - BINARY NUMBERING SYSTEM
Learning Objectives Describe Numbering Systems: decimal, binary, octal, and hexadecimal. Describe how characters are stored in computer memory. Demonstrate the application of binary (Boolean) operations of AND, OR, NOT, and XOR on binary numbers. Illustrate the use of binary in a computer with a focus on IP addresses.
Numbering Systems Decimal Base 10 Binary Base 2 Octal Base 8 Hexadecimal Base 16
Base 10 System - Decimal Primary human numbering system Digits 0 9 Example: 1, 2, 10, 4,321
Base 2 System - Binary Native numbering system for digital computers Two digits: 0, 1 Each digit is a bit that represents on or off Eight bits is a byte; also known as an octet Example: 0, 1, 10, 101, 1100
Base 8 - Octal Digits 0 7 Examples: 1, 5, 112
Base 16 - Hexadecimal Digits 0 F Examples: 0, 1, 3FA7
Character Representation American Standard Code for Information Interchange (ASCII) Unicode An extension of ASCII EBCDIC - Discontinued
ASCII 7-bit 128 combinations
Extended ASCII 8-bit 256 combinations
Unicode Extended ASCII is not enough for international use One Unicode mapping uses 16 bits per character 65363 Combinations Unicode is a superset of ASCII The first 256 characters correspond exactly to the extended ASCII character set
Binary Operations NOT AND OR NAND NOR XOR Gate - A device that performs a basic operation on electrical signals Circuit - Gates combined to perform more complicated tasks
Binary Operations NOT A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output
Binary Operations AND An AND gate accepts two input signals If both are 1, the output is 1; otherwise, the output is 0
Binary Operations OR An OR gate accepts two input signals If both are 0, the output is 0; otherwise, the output is 1
Binary Operations NAND The NAND gate accepts two input signals If both are 1, the output is 0; otherwise, the output is 1
Binary Operations NOR The NOR gate accepts two input signals If both are 0, the output is 1; otherwise, the output is 0
Binary Operations XOR An XOR gate accepts two input signals If both are the same, the output is 0; otherwise, the output is 1
Review of Gate Processing A NOT gate inverts its single input An AND gate produces 1 if both input values are 1 An OR gate produces 0 if both input values are 0 An XOR gate produces 0 if input values are the same A NAND gate produces 0 if both inputs are 1 A NOR gate produces a 1 if both inputs are 0
Constructing Gates A transistor has three terminals A source A base An emitter, typically connected to a ground wire
Constructing Gates The easiest gates to create are the NOT, NAND, and NOR gates
Combinational Circuits Gates are combined into circuits by using the output of one gate as the input for another
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