EASA Part 66 Module 5.2 : Numbering System
- 2. Many number systems are in use in digital technology. The most common are : • Decimal • Binary • Octal • Hexadecimal
- 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. DECIMAL EXAMPLE • 3.1410 • 53210 • 1082410 • 64900010
- 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. BINARY EXAMPLE • 1110 • 1011110 • 1111011100 • 10000101111011
- 7. OCTAL SYSTEM • The octal number system has a base of eight • Eight possible digits: 0,1,2,3,4,5,6,7
- 8. OCTAL EXAMPLE • Octal Example • 5410 • 765421 • 1047664 • 4123170137
- 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. HEXADECIMAL EXAMPLE • BD • 452EA • E451B2CD3 • 35412BABE
- 11. NUMBERING CONVERSION OCTAL DECIMAL BINARY HEXADECIMAL
- 12. DECIMAL TO BINARY CONVERSION Reverse 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. DECIMAL TO BINARY CONVERSION Repeat Division Method : EG : 18110 181/2 = 90 balance 1 EG : 2710 90/2 = 45 balance 0 27/2 = 13 balance 1 45/2 = 22 balance 1 13/2 = 6 balance 1 22/2 = 11 balance 0 6/2 = 3 balance 0 11/2 = 5 balance 1 3/2 = 1 balance 1 5/2 = 2 balance 1 1/2 = 0 balance 1 2/2 = 1 balance 0 1/2 = 0 balance 1 Result : 2710= 110112 Result : 18110= 101101012
- 14. DECIMAL TO OCTAL CONVERSION Ex : 17710 Ex : 398510 177/8 = 22 balance 1 3985/8 = 498 balance 1 22/8 = 2 balance 6 498/8 = 62 balance 2 2/8 = 0 balance 2 62/8 = 7 balance 6 Result 17710 = 2618 7/8 = 0 balance 7 Result 398510 = 76218
- 15. DECIMAL TO HEXADECIMAL Ex : 37810 378/16 = 23 balance 10 = (A) 23/16 = 1 balance 7 1/16 = 0 balance 1 Result 37810 = 17A16
- 16. DECIMAL TO HEXADECIMAL Ex : 694210 6942/16 = 433 balance 14 = (E) 433/16 = 27 balance 1 27/16 = 1 balance 11 = (B) 1/16 = 0 balance 1 Result 37810 = 1B1E16
- 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. 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. BINARY TO HEXADECIMAL 0 0000 1 0001 2 0010 3 0011 4 0100 EXAMPLE : 5 0101 6 0110 7 0111 101 11012 = (101) (1101)2 = 5 D16 8 1000 9 1001 A 1010 11 1001 10112 = (11) (1001) (1011)2 = 3 9 B16 B 1011 C 1100 D 1101 1011 0010 11112 = (1011) (0010) (1111)2 = B 2 F16 E 1110 F 1111
- 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. 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. HEXADECIMAL TO DECIMAL • Example : • 2E16 = 2(161) + 14 (160) = 4610 • 9BC316 = 9(163) + 11 (162) +12 (161) +3 (160) = 3987510
- 23. HEXADECIMAL TO BINARY 0 0000 1 0001 2 0010 3 0011 • 5 D16 = (101) (1101)2 =101 11012 4 0100 5 0101 6 0110 • 3 9 B16 = (11) (1001) (1011)2 =11 1001 10112 7 0111 8 1000 9 1001 • B 2 F16 = (1011) (0010) (1111)2 =1011 0010 11112 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111
- 24. NUMBERING CONVERSION OCTAL Table (div 3 ) Table (div 3) X/2 DECIMAL BINARY (+2 x ) Table (div 4) Table (div 4) HEXADECIMAL
- 25. CONVERSION VALUE Binary - Hexa Power 2 0 0000 20 1 1 0001 Binary - Octal Power 8 21 2 2 0010 0 000 22 4 80 1 3 0011 1 001 23 8 81 8 4 0100 2 010 24 16 82 64 5 0101 6 0110 3 011 25 32 83 512 7 0111 4 100 26 64 84 4096 8 1000 5 101 27 128 85 32768 9 1001 6 110 28 256 86 262144 A 1010 7 111 29 512 87 2097152 B 1011 210 1024 C 1100 D 1101 E 1110 F 1111