NUMBER SYSTEMS

PREPARED BYAKSHAY JANI (116380307521)

ACKNOWLEDGEMENT WE ARE IMMENSLY GREATFUL TO OUR LECTURER AND PROJECT

GUIDE MR.VIREN VALAND, FOR HER INVALUABLE GUIDANCE WHICH GAVE US A DEEP INSIGHT ON THE SUBJECT. WITH HER KEEN INTEREST AND CONSTANT MORAL BOOSTING, WE ARE ABLE TO IMPLEMENT THE PROJECT SATISFACTORILY.

WE EXPRESS OUR VERY SINCERE THANKS TO COMPUTER ENGINEERING DEPT. FOR PROVIDING ADEQUATE FACILITIES TO COMPLETE OUR PROJECT.

WE ARE AGAIN CORDIALLY THANKFUL TO OUR C&E DEPARTMENT STAFF, FRIENDS AND OTHER PEOPLE WHO HAVE DIRECTLY OR INDIRECTLY HELPED US IN COMPLETION OF THIS PROJECT. 

LAST BUT NOT THE LEAST, WE ARE ALSO THANKFUL TO OUR FAMILY MEMBERS WHO ENGOURAGED AND SUPPORTED US ROUND THE CLOCK FOR THIS PROJECT.

Akshay JaniKaushal Soni

CERTIFICATEThis is to certify that AKSHAY JANI Student of computer Engineering, bearing Enrollment No: 116380307521 have satisfactorily completed his/her Seminar work as a part of course curriculum in Diploma Engineering semester III having a report title “ NUMBER SYSTEMS ”.

MR.VIREN VALANDLecturer, computer Dept.

PIETDS-2nd Shift, Limda.

PARUL INSTITUTE OF ENGINEERING & TECHNOLOGYCOMPUTER ENGG. DEPARTMENTLIMDA, VAGHODIA, VADODARA

CERTIFICATEThis is to certify that KAUSHAL SONI Student of computer Engineering, bearing Enrollment No: 116380307509 have satisfactorily completed his/her Seminar work as a part of course curriculum in Diploma Engineering semester III having a report title “ NUMBER SYSTEMS ”.

MR.VIREN VALANDLecturer, computer Dept.

PIETDS-2nd Shift, Limda.

PARUL INSTITUTE OF ENGINEERING & TECHNOLOGYCOMPUTER ENGG. DEPARTMENTLIMDA, VAGHODIA, VADODARA

Number Systems

Four number system

Decimal (10) Binary (2) Octal (8) Hexadecimal (16) ............

Counting . . . 2, 8, 10, 16Decimal Binary Octal Hexadecimal

0 00000 0 0

1 00001 1 1

2 00010 2 2

3 00011 3 3

4 00100 4 4

5 00101 5 5

6 00110 6 6

7 00111 7 7

8 01000 10 8

9 01001 11 9

10 01010 12 A

11 01011 13 B

12 01100 14 C

13 01101 15 D

14 01110 16 E

15 01111 17 F

16 10000 20 10

17 10001 21 11

18 10010 22 12

19 10011 23 13

Octal Number System Also known as the Base 8 System Uses digits 0 - 7 Readily converts to binary Groups of three (binary) digits can be used to

represent each octal digit Also uses multiplication and division

algorithms for conversion to and from base 10

Decimal to Octal Conversion

Convert 42710 to its octal equivalent:

427 / 8 = 53 R3 Divide by 8; R is LSD53 / 8 = 6 R5 Divide Q by 8; R is next digit6 / 8 = 0 R6 Repeat until Q = 0

6538

Octal to Decimal Conversion

Convert 6538 to its decimal equivalent:

6 5 3

82 81 80

384 + 40 + 3

xxx

42710

Positional Values

Products

Octal Digits

Octal to Binary Conversion

Each octal number converts to 3 binary digits

To convert 6538 to binary, just substitute code:

6 5 3

110 101 011

Hexadecimal Number System

Base 16 system

Uses digits 0-9 & letters A,B,C,D,E,F

Groups of four bitsrepresent eachbase 16 digit

Decimal to Hexadecimal Conversion

Convert 83010 to its hexadecimal equivalent:

830 / 16 = 51 R1451 / 16 = 3 R33 / 16 = 0 R3

33E16

= E in Hex

Hexadecimal to Decimal Conversion

Convert 3B4F16 to its decimal equivalent:

Hex Digits 3 B 4 Fxxx

163 162 161 160

12288 +2816 + 64 +15

15,18310

Positional Values

Products

x

Binary to Hexadecimal Conversion The easiest method for converting binary

to hexadecimal is to use a substitution code.

Each hex number converts to 4 binary digits

APPENDIXWe are specially thanxx to……..

MR.VIREN VALANDMR.R.P.AJWALIA

THANK YOU……..