SLIDES BASED ON NUMBER SYSTEM...

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 System
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 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 Number
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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 Number
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 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:
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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 System
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 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
Number
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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.
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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
Number
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 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
equivalent
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926310 = 242F16
Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11

19. Example 2: Convert 425910 to its hexadecimal
equivalent
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425910 = 10A316
Usha Mary Sharma, Dept of CS& IT, DBCET 10-Aug-11

20. TRY THIS:
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 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