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# EASA Part 66 Module 5.2 : Numbering System

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Describe numbering system in binary, decimal, octal, hexadecimal and its conversion.
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http://part66.blogspot.com

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### EASA Part 66 Module 5.2 : Numbering System

1. 1. 5.2 NUMBERING SYSTEMS
2. 2. Many number systems are in use in digitaltechnology.The most common are :• Decimal• Binary• Octal• Hexadecimal
3. 3. DECIMAL SYSTEM• Composed of 10 numerals or symbols• Using these symbols as digits of a number, can express any quantity.• Called the base-10 system because it has 10 digits.• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
4. 4. DECIMAL EXAMPLE• 3.1410• 53210• 1082410• 64900010
5. 5. BINARY SYSTEM• There are only two symbols or possible digit values, 0 and 1.• This base-2 system can be used to represent any quantity that can be represented in decimal or other base system
6. 6. BINARY EXAMPLE• 1110• 1011110• 1111011100• 10000101111011
7. 7. OCTAL SYSTEM• The octal number system has a base of eight• Eight possible digits: 0,1,2,3,4,5,6,7
8. 8. OCTAL EXAMPLE• Octal Example• 5410• 765421• 1047664• 4123170137
9. 9. HEXADECIMAL SYSTEM• The hexadecimal system uses base 16.• It uses the digits 0 through 9 plus the letters A, B, C, D, E, and F as the 16 digit symbols.• 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
10. 10. HEXADECIMAL EXAMPLE• BD• 452EA• E451B2CD3• 35412BABE
11. 11. NUMBERING CONVERSION OCTALDECIMAL BINARY HEXADECIMAL
12. 12. DECIMAL TO BINARY CONVERSIONReverse of Binary-To-Decimal Method : 20 21 22 23 24 25 26 27 28 29 1 2 4 8 16 32 64 128 256 512• 2710 = 16+8+0+2+1 = 11011• 18110 = 128+0+32+16+0+4+0+1 = 10110101
13. 13. DECIMAL TO BINARY CONVERSIONRepeat Division Method : EG : 18110 181/2 = 90 balance 1EG : 2710 90/2 = 45 balance 027/2 = 13 balance 1 45/2 = 22 balance 113/2 = 6 balance 1 22/2 = 11 balance 06/2 = 3 balance 0 11/2 = 5 balance 13/2 = 1 balance 1 5/2 = 2 balance 11/2 = 0 balance 1 2/2 = 1 balance 0 1/2 = 0 balance 1Result : 2710= 110112 Result : 18110= 101101012
14. 14. DECIMAL TO OCTAL CONVERSIONEx : 17710 Ex : 398510177/8 = 22 balance 1 3985/8 = 498 balance 122/8 = 2 balance 6 498/8 = 62 balance 22/8 = 0 balance 2 62/8 = 7 balance 6Result 17710 = 2618 7/8 = 0 balance 7 Result 398510 = 76218
15. 15. DECIMAL TO HEXADECIMALEx : 37810378/16 = 23 balance 10 = (A)23/16 = 1 balance 71/16 = 0 balance 1Result 37810 = 17A16
16. 16. DECIMAL TO HEXADECIMALEx : 6942106942/16 = 433 balance 14 = (E)433/16 = 27 balance 127/16 = 1 balance 11 = (B)1/16 = 0 balance 1Result 37810 = 1B1E16
17. 17. BINARY TO DECIMAL CONVERSION 20 21 22 23 24 25 26 27 28 29 1 2 4 8 16 32 64 128 256 512 110112 = 24+23+02+21+20 = 16+8+0+2+1 = 2710 101101012 = 27+06+25+24+03+22+01+20 = 128+0+32+16+0+4+0+1 = 18110
18. 18. BINARY TO OCTAL CONVERSION 0 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111• Example:• 100 111 0102 = (100) (111) (010)2 = 4 7 28• 1 101 0102 = (001) (101) (010)2 = 1 5 28
19. 19. BINARY TO HEXADECIMAL0 00001 00012 00103 00114 0100 EXAMPLE :5 01016 01107 0111 101 11012 = (101) (1101)2 = 5 D168 10009 1001A 1010 11 1001 10112 = (11) (1001) (1011)2 = 3 9 B16B 1011C 1100D 1101 1011 0010 11112 = (1011) (0010) (1111)2 = B 2 F16E 1110F 1111
20. 20. OCTAL TO DECIMAL CONVERSION• Example :• 2378 = 2(82)+ 3(81)+ 2(80) = 15910• 95348 = 9(83)+ 5(82)+ 3(81)+ 4(80) = 495610
21. 21. OCTAL TO BINARY CONVERSION 0 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111• Example:• 4 7 28 = (100) (111) (010)2 = 100 111 0102• 1 5 28 = (001) (101) (010)2 = 1 101 0102
22. 22. HEXADECIMAL TO DECIMAL• Example :• 2E16 = 2(161) + 14 (160) = 4610• 9BC316 = 9(163) + 11 (162) +12 (161) +3 (160) = 3987510
23. 23. HEXADECIMAL TO BINARY0 00001 00012 00103 0011 • 5 D16 = (101) (1101)2 =101 110124 01005 01016 0110 • 3 9 B16 = (11) (1001) (1011)2 =11 1001 101127 01118 10009 1001 • B 2 F16 = (1011) (0010) (1111)2 =1011 0010 11112A 1010B 1011C 1100D 1101E 1110F 1111
24. 24. NUMBERING CONVERSION OCTAL Table (div 3 ) Table (div 3) X/2DECIMAL BINARY (+2 x ) Table (div 4) Table (div 4) HEXADECIMAL
25. 25. CONVERSION VALUE Binary - Hexa Power 2 0 000020 1 1 0001 Binary - Octal Power 821 2 2 0010 0 00022 4 80 1 3 0011 1 00123 8 81 8 4 0100 2 01024 16 82 64 5 0101 6 0110 3 01125 32 83 512 7 0111 4 10026 64 84 4096 8 1000 5 10127 128 85 32768 9 1001 6 11028 256 86 262144 A 1010 7 11129 512 87 2097152 B 1011210 1024 C 1100 D 1101 E 1110 F 1111