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# De presantation

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• This slide lists the first twenty numbers in each of the four number systems (decimal, binary, octal, hexadecimal).This is the first time that students will have see A, B, C, D, E, &amp; F used in a “number” system. Remember from Unit 1 that a number system uses its number of symbols to designate values. Base 16 needs 16 unique symbols; 10 is not a unique symbol, it is two. Therefore, the letter A is used to stand for 10, B for 11, and so on.
• ### De presantation

1. 1.  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
2. 2. This is to certify that AKSHAY JANI Student of computer Engineering,bearing Enrollment No: 116380307521 have satisfactorily completedhis/her Seminar work as a part of course curriculum in DiplomaEngineering 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
3. 3. This is to certify that KAUSHAL SONI Student of computerEngineering, bearing Enrollment No: 116380307509 have satisfactorilycompleted his/her Seminar work as a part of course curriculum inDiploma Engineering semester III having a report title “ NUMBERSYSTEMS ”. MR.VIREN VALAND Lecturer, computer Dept. PIETDS-2nd Shift, Limda. PARUL INSTITUTE OF ENGINEERING & TECHNOLOGY COMPUTER ENGG. DEPARTMENT LIMDA, VAGHODIA, VADODARA
4. 4. Four number system  Decimal (10)  Binary (2)  Octal (8)  Hexadecimal (16)  ............
5. 5. 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
6. 6.  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
7. 7. 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
8. 8. Convert 6538 to its decimal equivalent: Octal Digits 6 5 3 x x x Positional Values 82 81 80 Products 384 + 40 + 3 42710
9. 9. Each octal number converts to 3 binary digits To convert 6538 to binary, just substitute code: 6 5 3 110 101 011
10. 10.  Base 16 system Uses digits 0-9 & letters A,B,C,D,E,F Groups of four bits represent each base 16 digit
11. 11. Convert 83010 to its hexadecimal equivalent: 830 / 16 = 51 R14 = E in Hex 51 / 16 = 3 R3 3 / 16 = 0 R3 33E16
12. 12. 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
13. 13.  Theeasiest method for converting binary to hexadecimal is to use a substitution code. Each hex number converts to 4 binary digits