Download - Number system
![Page 1: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/1.jpg)
NUMBER NUMBER SYSTEMSYSTEMNUMBER NUMBER SYSTEMSYSTEM
The mysterious world of numbers…
22
![Page 2: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/2.jpg)
AcknowledgementWe would like to thank AKP sir for giving us an opportunity to express ourselves on this enthusiastic project. Any accomplishment requires the effort of many people and this work is no different. Every group member has been an important part of this project. We also thank our friends for their ideas and co-operation they provided to us. We are grateful to all of them.
Thank you..
![Page 3: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/3.jpg)
A number is a mathematical object used in counting and measuring. Numerals are often used for labels, for ordering serial numbers, and for codes like ISBNs.
In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
![Page 4: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/4.jpg)
The number system we use on day-to-day basis in the decimal system , which is based on ten digits: zero through nine. As the decimal system is based on ten digits, it is said to be base -10 or radix-10. Outside of specialized requirement such as computing , base-10 numbering system have been adopted almost universally. The decimal system with which we are fated is a place-value system, which means that the value of a particular digit depends both on the itself and on its position within the number.
![Page 5: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/5.jpg)
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straight forward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.
Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds through each symbol, in increasing order. Decimal counting uses the symbols 0 through 9, while binary only uses the symbols 0 and 1.
![Page 6: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/6.jpg)
Archimedes :
He was a Greek mathematician. He was the first to compute the digits in the decimal expansion of π (pi). He showed that -
3.140845 < π < 3.142857
Archimed
es
![Page 7: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/7.jpg)
Conversion Among Bases
•The possibilities:
Hexadecimal
Decimal Octal
Binary
![Page 8: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/8.jpg)
Quick Example
2510 = 110012 = 318 =1916
Base
![Page 9: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/9.jpg)
Different conversions Different conversions possible:possible:
> Binary to decimal> Octal to decimal> Hexadecimal to decimal> Decimal to binary> Octal to binary> Hexadecimal to binary> Decimal to octal, etc..
![Page 10: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/10.jpg)
Technique◦ Multiply each bit by 2n, where n is the “weight” of
the bit◦ The weight is the position of the bit, starting from
0 on the right◦ Add the results
![Page 11: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/11.jpg)
1010112 => 1 x 20 = 11 x 21 = 20 x 22 = 01 x 23 = 80 x 24 = 01 x 25 = 32
4310
Bit “0”
![Page 12: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/12.jpg)
Octal to DecimalOctal to DecimalTechnique
◦Multiply each bit by 8n, where n is the “weight” of the bit
◦The weight is the position of the bit, starting from 0 on the right
◦Add the results
![Page 13: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/13.jpg)
7248 => 4 x 80 = 42 x 81 = 167 x 82 = 448
46810
![Page 14: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/14.jpg)
TechniqueMultiply each bit by 16n, where n is the
“weight” of the bitThe weight is the position of the bit, starting
from 0 on the rightAdd the results
![Page 15: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/15.jpg)
ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560
274810
![Page 16: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/16.jpg)
TechniqueDivide by two, keep track of the remainderFirst remainder is bit 0 (LSB, least-significant
bit)Second remainder is bit 1Etc.
![Page 17: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/17.jpg)
12510 = ?2
2 125 62 12 31 02 15 12 7 12 3 12 1 12 0 1
12510 = 11111012
![Page 18: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/18.jpg)
Fractions
Decimal to binary3.14579
.14579x 20.29158x 20.58316x 21.16632x 20.33264x 20.66528x 21.33056
etc.11.001001...
![Page 19: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/19.jpg)
Octal to BinaryOctal to BinaryTechnique
◦Convert each octal digit to a 3-bit equivalent binary representation
ExampleExample7058 = ?2
7 0 5
111 000 101
7058 = 1110001012
![Page 20: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/20.jpg)
TechniqueConvert each hexadecimal digit to a 4-bit
equivalent binary representation
![Page 21: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/21.jpg)
10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
![Page 22: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/22.jpg)
Common Powers (2 of 2)
Base 2Power Preface Symbol
210 kilo k
220 mega M
230 Giga G
Value
1024
1048576
1073741824
What is the value of “k”, “M”, and “G”?
In computing, particularly w.r.t. memory, the base-2 interpretation generally applies
![Page 23: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/23.jpg)
Example
/ 230 =
In the lab…1. Double click on My Computer2. Right click on C:3. Click on Properties
![Page 24: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/24.jpg)
Numbers are never ending. You look into it, you find a world of quantities, helping you in your daily chores.
It’s a simple yet hard to understand, you work on it, you are going to love it more and more.
Exploring it is the best option, so just enjoy it.
![Page 25: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/25.jpg)
![Page 26: Number system](https://reader038.vdocuments.us/reader038/viewer/2022102902/558a8bf8d8b42a125f8b45de/html5/thumbnails/26.jpg)
Project made and Compiled by ~
Sanjana PoddarSana Jahan
Ronodeep MazumdarRiya Debnath