This document discusses various methods of data representation in computers, including:
1. Numeric and non-numeric data types. Computers represent numeric data like integers and real numbers, as well as non-numeric data like letters and symbols.
2. Positional number systems like binary, decimal, octal and hexadecimal are used for efficient internal representation in computers. Conversion between different bases is also covered.
3. Fixed point number representation including signed magnitude, 1's complement, and 2's complement representations. Floating point number representation separates the mantissa and exponent is also discussed.
Introduction Artificial Intelligence a modern approach by Russel and Norvig 1Garry D. Lasaga
In computer science, artificial intelligence, sometimes called machine intelligence, is intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans and animals. - Wikipedia
Introduction Artificial Intelligence a modern approach by Russel and Norvig 1Garry D. Lasaga
In computer science, artificial intelligence, sometimes called machine intelligence, is intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans and animals. - Wikipedia
Intelligent Agent PPT ON SLIDESHARE IN ARTIFICIAL INTELLIGENCEKhushboo Pal
n artificial intelligence, an intelligent agent (IA) is an autonomous entity which acts, directing its activity towards achieving goals (i.e. it is an agent), upon an environment using observation through sensors and consequent actuators (i.e. it is intelligent).An intelligent agent is a program that can make decisions or perform a service based on its environment, user input and experiences. These programs can be used to autonomously gather information on a regular, programmed schedule or when prompted by the user in real time. Intelligent agents may also be referred to as a bot, which is short for robot.Examples of intelligent agents
AI assistants, like Alexa and Siri, are examples of intelligent agents as they use sensors to perceive a request made by the user and the automatically collect data from the internet without the user's help. They can be used to gather information about its perceived environment such as weather and time.
Infogate is another example of an intelligent agent, which alerts users about news based on specified topics of interest.
Autonomous vehicles could also be considered intelligent agents as they use sensors, GPS and cameras to make reactive decisions based on the environment to maneuver through traffic.
Examples of intelligent agents
AI assistants, like Alexa and Siri, are examples of intelligent agents as they use sensors to perceive a request made by the user and the automatically collect data from the internet without the user's help. They can be used to gather information about its perceived environment such as weather and time.
Infogate is another example of an intelligent agent, which alerts users about news based on specified topics of interest.
Autonomous vehicles could also be considered intelligent agents as they use sensors, GPS and cameras to make reactive decisions based on the environment to maneuver through traffic.
Register Reference Instructions are those instructions that refer the registers to retrieve data from or to deposit data at. Copy the link given below and paste it in new browser window to get more information on Register Reference Instructions:- http://www.transtutors.com/homework-help/computer-science/computer-architecture/register-reference-instructions/
It's part of Computer Organization And Architecture .Data representation is how to data represented in computer by using complements of number , float point ,fix point, so it's
slide is useful
Intelligent Agent PPT ON SLIDESHARE IN ARTIFICIAL INTELLIGENCEKhushboo Pal
n artificial intelligence, an intelligent agent (IA) is an autonomous entity which acts, directing its activity towards achieving goals (i.e. it is an agent), upon an environment using observation through sensors and consequent actuators (i.e. it is intelligent).An intelligent agent is a program that can make decisions or perform a service based on its environment, user input and experiences. These programs can be used to autonomously gather information on a regular, programmed schedule or when prompted by the user in real time. Intelligent agents may also be referred to as a bot, which is short for robot.Examples of intelligent agents
AI assistants, like Alexa and Siri, are examples of intelligent agents as they use sensors to perceive a request made by the user and the automatically collect data from the internet without the user's help. They can be used to gather information about its perceived environment such as weather and time.
Infogate is another example of an intelligent agent, which alerts users about news based on specified topics of interest.
Autonomous vehicles could also be considered intelligent agents as they use sensors, GPS and cameras to make reactive decisions based on the environment to maneuver through traffic.
Examples of intelligent agents
AI assistants, like Alexa and Siri, are examples of intelligent agents as they use sensors to perceive a request made by the user and the automatically collect data from the internet without the user's help. They can be used to gather information about its perceived environment such as weather and time.
Infogate is another example of an intelligent agent, which alerts users about news based on specified topics of interest.
Autonomous vehicles could also be considered intelligent agents as they use sensors, GPS and cameras to make reactive decisions based on the environment to maneuver through traffic.
Register Reference Instructions are those instructions that refer the registers to retrieve data from or to deposit data at. Copy the link given below and paste it in new browser window to get more information on Register Reference Instructions:- http://www.transtutors.com/homework-help/computer-science/computer-architecture/register-reference-instructions/
It's part of Computer Organization And Architecture .Data representation is how to data represented in computer by using complements of number , float point ,fix point, so it's
slide is useful
This slide provide the introduction to the computer , instruction formats and their execution, Common Bus System , Instruction Cycle, Hardwired Control Unit and I/O operation and handling of interrupt
Unsigned and Signed fixed point Addition and subtractionciyamala kushbu
This content covers second unit COMPUTER ARCHITECTURE AND ORGANIZATION framed as per syllabus of Anna University 2017 Regulation.. This upload covers what is fixed and floating point operations. In fixed point operations the unsigned and signed addition and subtraction has been covered .
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
1. 1Data Representation
Computer Organization Computer Architectures Lab
DATA REPRESENTATION
Data Types
Complements
Fixed Point Representations
Floating Point Representations
Other Binary Codes
Error Detection Codes
2. 2Data Representation
Computer Organization Computer Architectures Lab
DATA REPRESENTATION
Information that a Computer is dealing with
* Data
- Numeric Data
Numbers( Integer, real)
- Non-numeric Data
Letters, Symbols
* Relationship between data elements
- Data Structures
Linear Lists, Trees, Rings, etc
* Program(Instruction)
Data Types
3. 3Data Representation
Computer Organization Computer Architectures Lab
NUMERIC DATA REPRESENTATION
R = 10 Decimal number system, R = 2 Binary
R = 8 Octal, R = 16 Hexadecimal
Radix point(.) separates the integer
portion and the fractional portion
Data
Numeric data - numbers(integer, real)
Non-numeric data - symbols, letters
Number System
Nonpositional number system
- Roman number system
Positional number system
- Each digit position has a value called a weight
associated with it
- Decimal, Octal, Hexadecimal, Binary
Base (or radix) R number
- Uses R distinct symbols for each digit
- Example AR = an-1 an-2 ... a1 a0 .a-1…a-m
- V(AR ) =
Data Types
∑
−
−=
1n
mi
i
i Ra
4. 4Data Representation
Computer Organization Computer Architectures Lab
WHY POSITIONAL NUMBER SYSTEM IN THE DIGITAL
COMPUTERS ?
Major Consideration is the COST and TIME
- Cost of building hardware
Arithmetic and Logic Unit, CPU,Communications
- Time to processing
Arithmetic - Addition of Numbers - Table for Addition
* Non-positional Number System
- Table for addition is infinite
--> Impossible to build, very expensive even
if it can be built
* Positional Number System
- Table for Addition is finite
--> Physically realizable, but cost wise
the smaller the table size, the less
expensive --> Binary is favorable to Decimal
0 1
0 0 1
1 1 10
0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 1011
3 3 4 5 6 7 8 9 101112
4 4 5 6 7 8 9 10111213
5 5 6 7 8 9 1011121314
6 6 7 8 9 101112131415
7 7 8 9 10111213141516
8 8 9 1011121314151617
9 9 101112131415161718
Binary Addition Table
Decimal Addition Table
Data Types
6. 6Data Representation
Computer Organization Computer Architectures Lab
CONVERSION OF
BASES
Decimal to Base R number
Base R to Decimal Conversion
V(A) = Σ ak Rk
A = an-1 an-2 an-3 … a0 . a-1 … a-m
(736.4)8 = 7 x 82
+ 3 x 81
+ 6 x 80
+ 4 x 8-1
= 7 x 64 + 3 x 8 + 6 x 1 + 4/8 = (478.5)10
(110110)2 = ... = (54)10
(110.111)2 = ... = (6.785)10
(F3)16 = ... = (243)10
(0.325)6 = ... = (0.578703703 .................)10
- Separate the number into its integer and fraction parts and convert
each part separately.
- Convert integer part into the base R number
--> successive divisions by R and accumulation of the remainders.
- Convert fraction part into the base R number
--> successive multiplications by R and accumulation of integer
digits
Data Types
7. 7Data Representation
Computer Organization Computer Architectures Lab
EXAMPLE
Convert 41.687510 to base 2.
Integer = 41
41
20 1
10 0
5 0
2 1
1 0
0 1
Fraction = 0.6875
0.6875
x 2
1.3750
x 2
0.7500
x 2
1.5000
x 2
1.0000
(41)10 = (101001)2 (0.6875)10 = (0.1011)2
(41.6875)10 = (101001.1011)2
Convert (63)10 to base 5: (223)5
Convert (1863)10 to base 8: (3507)8
Convert (0.63671875)10 to hexadecimal: (0.A3)16
Exercise
Data Types
8. 8Data Representation
Computer Organization Computer Architectures Lab
COMPLEMENT OF NUMBERS
Two types of complements for base R number system:
- R's complement and (R-1)'s complement
The (R-1)'s Complement
Subtract each digit of a number from (R-1)
Example
- 9's complement of 83510 is 16410
- 1's complement of 10102 is 01012(bit by bit complement operation)
The R's Complement
Add 1 to the low-order digit of its (R-1)'s complement
Example
- 10's complement of 83510 is 16410 + 1 = 16510
- 2's complement of 10102 is 01012 + 1 = 01102
Complements
9. 9Data Representation
Computer Organization Computer Architectures Lab
FIXED POINT NUMBERS
Binary Fixed-Point Representation
X = xnxn-1xn-2 ... x1x0. x-1x-2 ... x-m
Sign Bit(xn): 0 for positive - 1 for negative
Remaining Bits(xn-1xn-2 ... x1x0. x-1x-2 ... x-m)
- Following 3 representations
Signed magnitude representation
Signed 1's complement representation
Signed 2's complement representation
Example: Represent +9 and -9 in 7 bit-binary number
Only one way to represent +9 ==> 0 001001
Three different ways to represent -9:
In signed-magnitude: 1 001001
In signed-1's complement: 1 110110
In signed-2's complement: 1 110111
Numbers: Fixed Point Numbers and Floating Point Numbers
In general, in computers, fixed point numbers are represented
either integer part only or fractional part only.
Fixed Point Representations
10. 10Data Representation
Computer Organization Computer Architectures Lab
CHARACTERISTICS OF 3 DIFFERENT REPRESENTATIONS
Complement
Signed magnitude: Complement only the sign bit
Signed 1's complement: Complement all the bits including sign bit
Signed 2's complement: Take the 2's complement of the number,
including its sign bit.
Maximum and Minimum Representable Numbers and Representation of Zero
X = xn xn-1 ... x0 . x-1 ... x-m
Signed Magnitude
Max: 2n
- 2-m
011 ... 11.11 ... 1
Min: -(2n
- 2-m
) 111 ... 11.11 ... 1
Zero: +0 000 ... 00.00 ... 0
-0 100 ... 00.00 ... 0
Signed 1’s Complement
Max: 2n
- 2-m
011 ... 11.11 ... 1
Min: -(2n
- 2-m
) 100 ... 00.00 ... 0
Zero: +0 000 ... 00.00 ... 0
-0 111 ... 11.11 ... 1
Fixed Point Representations
Signed 2’s Complement
Max: 2n
- 2-m
011 ... 11.11 ... 1
Min: -2n
100 ... 00.00 ... 0
Zero: 0 000 ... 00.00 ... 0
11. 11Data Representation
Computer Organization Computer Architectures Lab
ARITHMETIC ADDITION: SIGNED MAGNITUDE
[1] Compare their signs
[2] If two signs are the same ,
ADD the two magnitudes - Look out for an overflow
[3] If not the same , compare the relative magnitudes of the numbers and
then SUBTRACT the smaller from the larger --> need a subtractor to add
[4] Determine the sign of the result
6 0110
+) 9 1001
15 1111 -> 01111
9 1001
- ) 6 0110
3 0011 -> 00011
9 1001
-) 6 0110
- 3 0011 -> 10011
6 0110
+) 9 1001
-15 1111 -> 11111
6 + 9 -6 + 9
6 + (- 9) -6 + (-9)
Overflow 9 + 9 or (-9) + (-9)
9 1001
+) 9 1001
(1)0010overflow
Fixed Point Representations
12. 12Data Representation
Computer Organization Computer Architectures Lab
ARITHMETIC ADDITION: SIGNED 2’s
COMPLEMENT
Example
6 0 0110
9 0 1001
15 0 1111
-6 1 1010
9 0 1001
3 0 0011
6 0 0110
-9 1 0111
-3 1 1101
-9 1 0111
-9 1 0111
-18 (1)0 1110
Add the two numbers, including their sign bit, and discard any carry out of
leftmost (sign) bit
overflow9 0 1001
9 0 1001+)
+) +)
+) +)
18 1 0010 2 operands have the same sign
and the result sign changes
xn-1yn-1s’n-1 + x’n-1y’n-1sn-1
x’n-1y’n-1sn-1
(cn-1 ⊕ cn)
xn-1yn s’n-1
(cn-1 ⊕ cn)
Fixed Point Representations
13. 13Data Representation
Computer Organization Computer Architectures Lab
ARITHMETIC ADDITION: SIGNED 1’s
COMPLEMENT
Add the two numbers, including their sign bits.
- If there is a carry out of the most significant (sign) bit, the result is
incremented by 1 and the carry is discarded.
6 0 0110
-9 1 0110
-3 1 1100
-6 1 1001
9 0 1001
(1) 0(1)0010
1
3 0 0011
+) +)
+)
end-around carry
-9 1 0110
-9 1 0110
(1)0 1100
1
0 1101
+)
+)
9 0 1001
9 0 1001
1 (1)0010
+)
overflow
Example
not overflow (cn-1 ⊕ cn) = 0
(cn-1 ⊕ cn)
Fixed Point Representations
14. 14Data Representation
Computer Organization Computer Architectures Lab
COMPARISON OF REPRESENTATIONS
* Easiness of negative conversion
S + M > 1’s Complement > 2’s Complement
* Hardware
- S+M: Needs an adder and a subtractor for Addition
- 1’s and 2’s Complement: Need only an adder
* Speed of Arithmetic
2’s Complement > 1’s Complement(end-around C)
* Recognition of Zero
2’s Complement is fast
Fixed Point Representations
15. 15Data Representation
Computer Organization Computer Architectures Lab
ARITHMETIC SUBTRACTION
Take the complement of the subtrahend (including the sign bit)
and add it to the minuend including the sign bits.
( ± A ) - ( - B ) = ( ± A ) + B
( ± A ) - B = ( ± A ) + ( - B )
Fixed Point Representations
Arithmetic Subtraction in 2’s complement
16. 16Data Representation
Computer Organization Computer Architectures Lab
FLOATING POINT NUMBER REPRESENTATION
* The location of the fractional point is not fixed to a certain location
* The range of the representable numbers is wide
F = EM
mn ekek-1 ... e0 mn-1mn-2 … m0 . m-1 … m-m
sign exponent mantissa
- Mantissa
Signed fixed point number, either an integer or a fractional number
- Exponent
Designates the position of the radix point
Decimal Value
V(F) = V(M) * RV(E) M: Mantissa
E: Exponent
R: Radix
Floating Point Representation
17. 17Data Representation
Computer Organization Computer Architectures Lab
FLOATING POINT NUMBERS
0 .1234567 0 04
sign sign
mantissa exponent
==> +.1234567 x 10+04
Example
A binary number +1001.11 in 16-bit floating point number representation
(6-bit exponent and 10-bit fractional mantissa)
0 0 00100 100111000
0 0 00101 010011100
Example
Note:
In Floating Point Number representation, only Mantissa(M) and
Exponent(E) are explicitly represented. The Radix(R) and the position
of the Radix Point are implied.
Exponent MantissaSign
or
Floating Point Representation
18. 18Data Representation
Computer Organization Computer Architectures Lab
CHARACTERISTICS OF FLOATING POINT NUMBER REPRESENTATIONS
Normal Form
- There are many different floating point number representations of
the same number
--> Need for a unified representation in a given computer
- the most significant position of the mantissa contains a non-zero digit
Representation of Zero
- Zero
Mantissa = 0
- Real Zero
Mantissa = 0
Exponent
= smallest representable number
which is represented as
00 ... 0
<-- Easily identified by the hardware
Floating Point Representation
19. 19Data Representation
Computer Organization Computer Architectures Lab
INTERNAL REPRESENTATION AND EXTERNAL REPRESENTATION
CPU
Memory
Internal
Representation
Human
Device
Another
Computer
External
Representation
External
Representation
External
Representation
External Representations Internal Representations
- Presentability - Efficiency
- Efficiency Memory space
Communication Processing time
Reliability - Easy to convert to
- Easy to handle external representation
- BCD, ASCII, EBCDIC - Fixed and Floating points
20. 20Data Representation
Computer Organization Computer Architectures Lab
EXTERNAL REPRESENTATION
Decimal BCD Code
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
Numbers
Most of numbers stored in the computer are eventually changed
by some kinds of calculations
--> Internal Representation for calculation efficiency
--> Final results need to be converted to as External Representation
for presentability
Alphabets, Symbols, and some Numbers
Elements of these information do not change in the course of processing
--> No needs for Internal Representation since they are not used
for calculations
--> External Representation for processing and presentability
Example
Decimal Number: 4-bit Binary Code
BCD(Binary Coded Decimal)
External Representations
21. 21Data Representation
Computer Organization Computer Architectures Lab
OTHER DECIMAL CODES
Decimal BCD(8421) 2421 84-2-1 Excess-3
0 0000 0000 0000 0011
1 0001 0001 0111 0100
2 0010 0010 0110 0101
3 0011 0011 0101 0110
4 0100 0100 0100 0111
5 0101 1011 1011 1000
6 0110 1100 1010 1001
7 0111 1101 1001 1010
8 1000 1110 1000 1011
9 1001 1111 1111 1100 d3 d2 d1 d0: symbol in the codes
BCD: d3 x 8 + d2 x 4 + d1 x 2 + d0 x 1
==> 8421 code.
2421: d3 x 2 + d2 x 4 + d1 x 2 + d0 x 1
84-2-1: d3 x 8 + d2 x 4 + d1 x (-2) + d0 x (-1)
Excess-3: BCD + 3
Note: 8,4,2,-2,1,-1 in this table is the weight
associated with each bit position.
BCD: It is difficult to obtain the 9's complement.
However, it is easily obtained with the other codes listed above.
==> Self-complementing codes
External Representations
23. 23Data Representation
Computer Organization Computer Architectures Lab
GRAY CODE - ANALYSIS
Letting gngn-1 ... g1 g0 be the (n+1)-bit Gray code
for the binary number bnbn-1 ... b1b0
gi = bi ⊕ bi+1 , 0 ≤ i ≤ n-1
gn = bn
and
bn-i = gn ⊕ gn-1 ⊕ . . . ⊕ gn-i
bn = gn
0 0 0 0 00 0 000
1 0 1 0 01 0 001
1 1 0 11 0 011
1 0 0 10 0 010
1 10 0 110
1 11 0 111
1 01 0 101
1 00 0 100
1 100
1 101
1 111
1 010
1 011
1 001
1 101
1 000
The Gray code has a reflection property
- easy to construct a table without calculation,
- for any n: reflect case n-1 about a
mirror at its bottom and prefix 0 and 1
to top and bottom halves, respectively
Reflection of Gray codes
Note:
Other Binary codes
ε
24. 24Data Representation
Computer Organization Computer Architectures Lab
CHARACTER REPRESENTATION ASCII
ASCII (American Standard Code for Information Interchange) Code
Other Binary codes
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
NUL
SOH
STX
ETX
EOT
ENQ
ACK
BEL
BS
HT
LF
VT
FF
CR
SO
SI
SP
!
“
#
$
%
&
‘
(
)
*
+
,
-
.
/
0
1
2
3
4
5
6
7
8
9
:
;
<
=
>
?
@
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
[
]
m
n
‘
a
b
c
d
e
f
g
h
I
j
k
l
m
n
o
P
q
r
s
t
u
v
w
x
y
z
{
|
}
~
DEL
0 1 2 3 4 5 6 7
DLE
DC1
DC2
DC3
DC4
NAK
SYN
ETB
CAN
EM
SUB
ESC
FS
GS
RS
US
LSB
(4 bits)
MSB (3 bits)
25. 25Data Representation
Computer Organization Computer Architectures Lab
CONTROL CHARACTER REPRESENTAION (ACSII)
NUL Null
SOH Start of Heading (CC)
STX Start of Text (CC)
ETX End of Text (CC)
EOT End of Transmission (CC)
ENQ Enquiry (CC)
ACK Acknowledge (CC)
BEL Bell
BS Backspace (FE)
HT Horizontal Tab. (FE)
LF Line Feed (FE)
VT Vertical Tab. (FE)
FF Form Feed (FE)
CR Carriage Return (FE)
SO Shift Out
SI Shift In
DLE Data Link Escape (CC)
(CC) Communication Control
(FE) Format Effector
(IS) Information Separator
Other Binary codes
DC1 Device Control 1
DC2 Device Control 2
DC3 Device Control 3
DC4 Device Control 4
NAK Negative Acknowledge (CC)
SYN Synchronous Idle (CC)
ETB End of Transmission Block (CC)
CAN Cancel
EM End of Medium
SUB Substitute
ESC Escape
FS File Separator (IS)
GS Group Separator (IS)
RS Record Separator (IS)
US Unit Separator (IS)
DEL Delete
26. 26Data Representation
Computer Organization Computer Architectures Lab
ERROR DETECTING CODES
Parity System
- Simplest method for error detection
- One parity bit attached to the information
- Even Parity and Odd Parity
Even Parity
- One bit is attached to the information so that
the total number of 1 bits is an even number
1011001 0
1010010 1
Odd Parity
- One bit is attached to the information so that
the total number of 1 bits is an odd number
1011001 1
1010010 0
Error Detecting codes
27. 27Data Representation
Computer Organization Computer Architectures Lab
Parity Bit Generation
For b6b5... b0(7-bit information); even parity bit beven
beven = b6 ⊕ b5 ⊕ ... ⊕ b0
For odd parity bit
bodd = beven ⊕ 1 = beven
PARITY BIT GENERATION