Binary, decimal, hexadecimal number representation, converting between
Applications and relative advantages
Addition and subtraction in binary, range of n-bit numbers
A digital system can understand positional number system only where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.
Introduction
Number Systems
Types of Number systems
Inter conversion of number systems
Binary addition ,subtraction, multiplication and
division
Complements of binary number(1’s and 2’s
complement)
Grey code, ASCII, Ex
3,BCD
A digital system can understand positional number system only where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.
Introduction
Number Systems
Types of Number systems
Inter conversion of number systems
Binary addition ,subtraction, multiplication and
division
Complements of binary number(1’s and 2’s
complement)
Grey code, ASCII, Ex
3,BCD
Contents:
1.What is number system?
2.Conversions of number from one radix to another
3.Complements (1's, 2's, 9's, 10's)
4.Binary Arithmetic ( Addition, subtraction, multiplication, division)
Chapter 2 Data Representation on CPU (part 1)Frankie Jones
This topic introduces the numbering systems: decimal, binary, octal and hexadecimal. The topic covers the conversion between numbering systems, binary arithmetic, one's complement, two's complement, signed number and coding system. This topic also covers the digital logic components.
Inductive programming incorporates all approaches which are concerned with learning programs or algorithms from incomplete (formal) specifications. Possible inputs in an IP system are a set of training inputs and corresponding outputs or an output evaluation function, describing the desired behavior of the intended program, traces or action sequences which describe the process of calculating specific outputs, constraints for the program to be induced concerning its time efficiency or its complexity, various kinds of background knowledge such as standard data types, predefined functions to be used, program schemes or templates describing the data flow of the intended program, heuristics for guiding the search for a solution or other biases.
Output of an IP system is a program in some arbitrary programming language containing conditionals and loop or recursive control structures, or any other kind of Turing-complete representation language.
In many applications the output program must be correct with respect to the examples and partial specification, and this leads to the consideration of inductive programming as a special area inside automatic programming or program synthesis, usually opposed to 'deductive' program synthesis, where the specification is usually complete.
In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intelligence. A distinctive feature is the number of examples or partial specification needed. Typically, inductive programming techniques can learn from just a few examples.
The diversity of inductive programming usually comes from the applications and the languages that are used: apart from logic programming and functional programming, other programming paradigms and representation languages have been used or suggested in inductive programming, such as functional logic programming, constraint
programming, probabilistic programming
Research on the inductive synthesis of recursive functional programs started in the early 1970s and was brought onto firm theoretical foundations with the seminal THESIS system of Summers[6] and work of Biermann.[7] These approaches were split into two phases: first, input-output examples are transformed into non-recursive programs (traces) using a small set of basic operators; second, regularities in the traces are searched for and used to fold them into a recursive program. The main results until the mid 1980s are surveyed by Smith.[8] Due to
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
2. Topics: Number systems, and binary arithmetic
• Binary, decimal, hexadecimal number representation, converting
between
• Applications and relative advantages
• Addition and subtraction in binary, range of n-bit numbers
• Sample activities:
• Paired activity: Exercises converting between the different number
systems
• Group activity: Discuss relative advantages and disadvantages
between applications
• Individual activity: Calculations using different number bases
14/5/2019 Digital Principles_HND L4 2
3. Number Systems
• Common types of number systems used in Digital and
Computer Technology:
• Decimal (base 10)
• Binary (base 2)
• Octal (base 8 but obsolete)
• Hexadecimal (base 16)
Digital Principles_HND L414/5/2019 4
4. Positional values ( weights)
104 103 102 101 100
Decimal Numbering System
7 3 461
• Has ten symbols: ‘0’ through ‘9’
• Each position in the symbol sequence is
weighted by a factor of ten more than the
one to the right
• E.g.:
7316410 = 7 × 104 + 3 × 103 + 1 × 102 + 6 × 101 + 4 × 100
Digital Principles_HND L414/5/2019 5
5. Positional values ( weights)
24 23 22 21 20
• Has two symbols: ‘0’ and ‘1’
• Each position weighted by a factor of two
more than the one to the right.
• E.g.:
101012 = 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20 = 2110
Binary Numbering System
1 0 101
Digital Principles_HND L414/5/2019 6
6. • The least significant bit of the binary
representation of Even quantities is ‘0’
and Odd quantities is ‘1’.
• Doubling a decimal value will have the
equivalent effect of shifting the binary
value to the left by one position
E.g.:
210 = 00102, 410 = 01002 , 810 = 10002
Counting in Binary System
Decimal System Binary System
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111Digital Principles_HND L414/5/2019 7
7. Range of Binary Representation
• What is the largest number that can be represented
using N bits?
• The more bits, the bigger the number
• E.g. If no. of bits, N = 8 , when all the bits are 1s , then the
largest number is 255
• Alternatively , it can be calculated as shown below
2N – 1 = 28 – 1
= 25510
= 111111112
Digital Principles_HND L414/5/2019 8
8. 1)Justify whether the binary number 110012 is equal to 2510 (decimal
form).
2)What is the largest number that can be represented using 8 bits?
Show your steps clearly.
3) Convert the binary number 1011 0101 1100 01102 to its
hexadecimal form (base 16)
14/5/2019 Digital Principles_HND L4 9
9. Justify whether the binary number 110012
is equal to 2510 (decimal form).
• Yes.
• 1x24 + 1x23 + 0x22 + 0x21 + 1x20
• = 16 + 8 + 0 + 0 + 1
• = 2510
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10. What is the largest number that can be
represented using 6 bits? Show your steps clearly.
• 255
• 26 – 1 = 25510
• = 111111112
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11. Convert the binary number 1011 0101 1100 01102 to its hexadecimal
form (base 16).
• 1011 = 11 (B)
• 0101 = 5
• 1100 = 12 (C)
• 0110 = 6
• 1011 0101 1101 01002 = B5C616
14/5/2019 Digital Principles_HND L4 12
12. Positional values ( weights)
163 162 161 160
F DEE
Hexadecimal Numbering System
• Has 16 symbols: ‘0’ through ‘F’
• Each position weighted by a factor of
sixteen more than the symbol to the right.
• E.g.:
FEED16 = 15×163 + 14×162 + 14×161 + 13×160 = 6526110
Digital Principles_HND L414/5/2019 13
13. Decimal-to-Binary Conversion
• Various methods can be used, 2 of which are:
• Sum-of-Weight Method
• Repeated Division-by-2 Method
Digital Principles_HND L414/5/2019 15
16. 14/5/2019 Digital Principles_HND L4 18
Convert decimal 35 into Binary number.
Divide 35 by 2: 17 remainder 1
Divide 17 by 2: 8 remainder 1
Divide 8 by 2: 4 remainder 0
Divide 4 by 2: 2 remainder 0
Divide 2 by 2: 1 remainder 0
Divide 1 by 2: 0 remainder 1
►Put together the remainders from bottom to top:
► Decimal 3510 ≡ Binary 1000112
17. 14/5/2019 Digital Principles_HND L4 19
The same method can be used to convert to
hexadecimal (16-symbol) numbers too.
Let us consider again 3510.
Divide 35 by 16:2 remainder 3
Divide 2 by 16: 0 remainder 2
►Put together the remainders from bottom to
top:
► 3510 ≡ 2316
18. Hexadecimal-to-Binary Conversion
• Convert each digit of the Hexadecimal System number
to its 4-bit Binary System representation
• E.g.: Hexadecimal System Binary System
20016 0010 0000 00002
3E16 0011 11102
1FA16 0001 1111 10102
123D16 0001 0010 0011 11012
Digital Principles_HND L414/5/2019 20
19. 14/5/2019 Digital Principles_HND L4 21
System: A B C
Number of symbols used: 10 2 16
Symbol of smallest value: 0 0 0
Symbol of largest value 9 1 F
20. 14/5/2019 Digital Principles_HND L4 22
Decimal System Binary System Hexadecimal System
0 0 0
1 1 1
2 ? 2
3 11 ?
4 100 4
5 ? ?
6 ? ?
7 111 7
8 ? ?
9 1001 ?
10 1010 A
11 ? ?
12 1100 C
13 ? ?
14 ? ?
15 1111 F
16 ? ?
21. 14/5/2019 Digital Principles_HND L4 23
Decimal System Binary System Hexadecimal System
252 1111 1100 FC
253 1111 1101 FD
254 1111 1110 FE
255 ? ?
256 1 0000 0000 100
257 ? ?
258 ? 102
.
.
.
.
.
.
.
.
.
1023 11 1111 1111 3FF
1024 ? 400
1025 ? ?
22. 14/5/2019 Digital Principles_HND L4 25
Now, convert the binary number systems to decimal
system.
(i) 10112
= (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20)
= 8 + 2 + 1
= 1110
(ii) 101012
= (1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20)
=16 + 0 + 4 + 0 + 1
=2110
23. 14/5/2019 Digital Principles_HND L4 27
Convert the following binary numbers to decimal:
a) 0110
b) 1010
c) 1111 0101
d) 1010 1011
Convert the following decimal numbers to its binary equivalent
representation.
a) 7
b) 14
c) 28
24. 14/5/2019 Digital Principles_HND L4 28
Convert the following hexadecimal numbers into its
decimal AND binary representation.
a) 3C
b) 50F
c) BEEF
25. 14/5/2019 Digital Principles_HND L4 29
Converting Binary (base 2) to Decimal system (base 10)
10112 = (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20)
= 8 + 0 + 2 + 1
= 1110
Converting Hexadecimals (base 16) to Decimal system (base 10)
A316 = (A16 x 161) + (316 x 160)
= (10 x 161) + (3 x 160)
= 160 + 3
= 16310
26. How Are They Different?
• Decimal vs Hexadecimal vs Octal vs Binary
Decimal Hexadecimal Octal Binary
Base 10 16 8 2
Symbols 0 – 9 0 – 9 , A – F 0 – 7 0 – 1
Number of
symbols
10 16 8 2
Highest
Symbol Value
9 F 7 1
Digital Principles_HND L414/5/2019 30