W 9 numbering system
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This document discusses various topics related to digital representation of data including: 1. The differences between FAT32 and NTFS file systems and their advantages and limitations. 2. How data is represented digitally using coding schemes like ASCII and converted between binary and other number systems. 3. An overview of different numbering systems including binary, decimal, octal and hexadecimal; and how to convert between them.
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W 9 numbering system
- 11. Types of Positional Number Systems No No 0, 1, … 9, A, B, … F 16 Hexa-decimal No No 0, 1, … 7 8 Octal Yes No 0, 1 2 Binary No Yes 0, 1, … 9 10 Decimal Used in computers? Used by humans? Symbols Base System
- 16. Binary Number System Base (Radix) 2 Digits 0, 1 e.g. 1110 2 The digit 1 in the third position from the right represents the value 4 and the digit 1 in the fourth position from the right represents the value 8. 1 8=2 3 1 1 0 4=2 2 2=2 1 1=2 0
- 17. Decimal Number System Base (Radix) 10 Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 e.g. 7475 10 The magnitude represented by a digit is decided by the position of the digit within the number. For example the digit 7 in the left-most position of 7475 counts for 7000 and the digit 7 in the second position from the right counts for 70. 7 1000 100 4 7 5 1 10
- 18. Octal Number System Base (Radix) 8 Digits 0, 1, 2, 3, 4, 5, 6, 7 e.g. 1623 8 The digit 2 in the second position from the right represents the value 16 and the digit 1 in the fourth position from the right represents the value 512. 1 512=8 3 6 64=8 2 2 8=8 1 3 1=8 0
- 19. Hexadecimal Number System Base (Radix) 16 Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F e.g. 2F4D 16 The digit F in the third position from the right represents the value 3840 and the digit D in the first position from the right represents the value 1. 2 4096=16 3 F 256=16 2 4 16=16 1 D 1=16 0
- 21. Quantities/Counting (1 of 3) 7 7 111 7 6 6 110 6 5 5 101 5 4 4 100 4 3 3 11 3 2 2 10 2 1 1 1 1 0 0 0 0 Hexa- decimal Octal Binary Decimal
- 22. Quantities/Counting (2 of 3) F 17 1111 15 E 16 1110 14 D 15 1101 13 C 14 1100 12 B 13 1011 11 A 12 1010 10 9 11 1001 9 8 10 1000 8 Hexa- decimal Octal Binary Decimal
- 23. Quantities/Counting (3 of 3) Etc. 17 27 10111 23 16 26 10110 22 15 25 10101 21 14 24 10100 20 13 23 10011 19 12 22 10010 18 11 21 10001 17 10 20 10000 16 Hexa- decimal Octal Binary Decimal
- 25. Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base
- 26. Decimal to Decimal (just for fun) Hexadecimal Decimal Octal Binary
- 27. 125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight
- 28. Binary to Decimal Hexadecimal Decimal Octal Binary
- 30. Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0”
- 31. Octal to Decimal Hexadecimal Decimal Octal Binary
- 33. Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10
- 34. Hexadecimal to Decimal Hexadecimal Decimal Octal Binary
- 36. Example ABC 16 => C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10
- 37. Decimal to Binary Hexadecimal Decimal Octal Binary
- 39. Example 125 10 = ? 2 125 10 = 1111101 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1
- 40. Octal to Binary Hexadecimal Decimal Octal Binary
- 42. Example 705 8 = 111000101 2 705 8 = ? 2 7 0 5 111 000 101
- 43. Hexadecimal to Binary Hexadecimal Decimal Octal Binary
- 45. Example 10AF 16 = ? 2 10AF 16 = 0001000010101111 2 1 0 A F 0001 0000 1010 1111
- 46. Decimal to Octal Hexadecimal Decimal Octal Binary
- 48. Example 1234 10 = ? 8 8 1234 154 2 1234 10 = 2322 8 8 19 2 8 2 3 8 0 2
- 49. Decimal to Hexadecimal Hexadecimal Decimal Octal Binary
- 51. Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4
- 52. Binary to Octal Hexadecimal Decimal Octal Binary
- 54. Example 1011010111 2 = ? 8 1011010111 2 = 1327 8 1 011 010 111 1 3 2 7
- 55. Binary to Hexadecimal Hexadecimal Decimal Octal Binary
- 58. Octal to Hexadecimal Hexadecimal Decimal Octal Binary
- 60. Example 1076 8 = ? 16 1076 8 = 23E 16 1 0 7 6 001 000 111 110 2 3 E
- 61. Hexadecimal to Octal Hexadecimal Decimal Octal Binary
- 63. Example 1F0C 16 = ? 8 1 7 4 1 4 1F0C 16 = 17414 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4
- 64. Exercise – Convert ... Answer Don’t use a calculator! 1AF 703 1110101 33 Hexa- decimal Octal Binary Decimal
- 67. Example In the lab… 1. Double click on My Computer 2. Right click on C: 3. Click on Properties / 2 30 =
Editor's Notes
- A file system is the underlying structure a computer uses to organize data on a hard disk.
- A file system is the underlying structure a computer uses to organize data on a hard disk. NTFS is the preferred file system.
- “ A number system is a term used for a set of different symbols or digits, which represent a numerical value.”
- It is also called natural number system, because it is natural to humans.