Number systems(D.B.C.E.T)
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  • 1. Usha Mary Sharma, Dept of CS& IT, DBCET 1 NUMBER SYSTEMS Continuation of the first lecture … ECE-B first semester.10-Aug-11
  • 2. The Octal Number System2  The base of the octal number system is eight.  From right to left, the successive positions of the octal number are weighted 1, 8, 64, 512, etc  A list of the first several powers of 8 follows: 80 = 1 81 = 8 82 = 64 83 = 512 84 = 4096 85 = 32768 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 3. Decimal numbers with their octal equivalents:3 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 4. Convert Octal Number to Decimal Number4 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 5. 5  determine the value of the octal number 16018 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 6. Solution :6 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 7. TRY THIS:7 Convert the following octal numbers to their decimal equivalents: (a) 5 3 68 Answer: 35010 (b) 1 1 6 38 Answer: 62710 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 8. Converting a Decimal Number to an Octal Number8  Use the remainder method . (1) Divide the decimal number by the base (in the case of octal, divide by 8). (2) Indicate the remainder to the right. (3) Continue dividing into each quotient (and indicating the remainder) until the divide operation produces a zero quotient. (4) The base 8 number is the numeric remainder reading from the last division to the first (if you start at the bottom, the answer will read from top to bottom). Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 9. Example 1: Convert the decimal number 46510 to its octal equivalent:9  Solution: 46510 = 7218 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 10. Example 2: Convert the decimal number 254810 to its octal equivalent:10  Solution: 254810 = 47648 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 11. TRY THIS:11 Convert the following decimal numbers to their octal equivalents: (a) 300210 Answer: 57628 (b) 651210 Answer: 145608 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 12. The Hexadecimal Number System12  The hexadecimal number system has base 16.  From right to left, the successive positions of the hexadecimal number are weighted 1, 16, 256, 4096, 65536, etc. 160 = 1 161 = 16 162 = 256 163 = 4096 164 = 65536  The hexadecimal number system uses not only the Arabic numerals 0 through 9, but also uses the letters A, B, C, D, E, and F. Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 13. Decimal numbers with their hexadecimal equivalents:13 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 14. Converting a Hexadecimal Number to a Decimal Number14 Example 1: Convert the hexadecimal number 20B316 to its decimal equivalent Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 15. Example 2: Convert the hexadecimal number 12AE516 to its decimal equivalent.15 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 16. TRY THIS.16 Convert the following hexadecimal numbers to their decimal equivalents: (a) 2 4 3 F16 Answer: 927910 (b) B E E F16 Answer: 4887910 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 17. Converting a Decimal Number to a Hexadecimal Number17  Use the remainder method.  the remainder method involves the following four steps: (1) Divide the decimal number by the base (in the case of hexadecimal, divide by 16). (2) Indicate the remainder to the right. If the remainder is between 10 and 15, indicate the corresponding hex digit A through F. (3) Continue dividing into each quotient (and indicating the remainder) until the divide operation produces a zero quotient. (4) The base 16 number is the numeric remainder reading from the last division to the first. Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 18. Example 1: Convert 926310 to its hexadecimal equivalent18 926310 = 242F16 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 19. Example 2: Convert 425910 to its hexadecimal equivalent19 425910 = 10A316 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 20. TRY THIS:20  Convert the following decimal numbers to their hexadecimal equivalents (a) 6949810 Answer: 10F7A16 (b) 11426710 Answer: 1BE5B16 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11
  • 21. Revision:21 Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11