2.  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 Jani
Kaushal Soni

3. This 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 VALAND
Lecturer, computer Dept.
PIETDS-2nd Shift, Limda.
PARUL INSTITUTE OF ENGINEERING & TECHNOLOGY
COMPUTER ENGG. DEPARTMENT
LIMDA, VAGHODIA, VADODARA

4. This 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 VALAND
Lecturer, computer Dept.
PIETDS-2nd Shift, Limda.
PARUL INSTITUTE OF ENGINEERING & TECHNOLOGY
COMPUTER ENGG. DEPARTMENT
LIMDA, VAGHODIA, VADODARA

5. Four number system
 Decimal (10)
 Binary (2)
 Octal (8)
 Hexadecimal (16)
 ............

6. Decimal 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

7.  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

8. Convert 42710 to its octal equivalent:
427 / 8 = 53 R3 Divide by 8; R is LSD
53 / 8 = 6 R5 Divide Q by 8; R is next
digit
6 / 8 = 0 R6 Repeat until Q = 0
6538

9. Convert 6538 to its decimal equivalent:
Octal Digits 6 5 3
x x x
Positional Values
82 81 80
Products 384 + 40 + 3
42710

10. Each octal number converts to 3 binary digits
To convert 6538 to binary, just substitute code:
6 5 3
110 101 011

11.  Base 16 system
 Uses digits 0-9 &
letters A,B,C,D,E,F
 Groups of four bits
represent each
base 16 digit

12. Convert 83010 to its hexadecimal equivalent:
830 / 16 = 51 R14
= E in Hex
51 / 16 = 3 R3
3 / 16 = 0 R3
33E16

13. Convert 3B4F16 to its decimal equivalent:
Hex Digits
3 B 4 F
x x x x
Positional Values
163 162 161 160
Products 12288 +2816 + 64 +15
15,18310

14.  Theeasiest method for converting binary to
hexadecimal is to use a substitution code.
 Each hex number converts to 4 binary digits