1. Monika Gope Lecturer IICT, KUET
Number System…
Monika Gope
Lecturer
IICT, KUET

2. Inside The Computer
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3. Decimal to Binary
Technique 1:
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Step 1

4. Decimal to Binary
Technique 1:
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Step 2

5. Decimal to Binary
Technique 1:
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Steps

6. Decimal to Binary
Technique 1:
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Steps

7. Decimal to Binary
Technique 2:
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Step 1

8. Decimal to Binary
Technique 2:
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Step 2

9. Decimal to Binary
Technique 2:
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Step 3

10. Decimal to Binary
Technique 2:
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Step 4

11. Decimal to Binary
Technique 2:
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Step 5

12. Decimal to Binary
Technique 2:
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Step 6

13. Decimal to Binary
Technique 2:
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Step 7

14. Decimal to Binary
Technique 2:
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Step 8

15. Decimal to Binary
Technique 2:
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Step 9

16. Binary to Decimal
Technique 1:
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Step 1

17. Binary to Decimal
Technique 1:
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Step 2

18. Binary to Decimal
Technique 1:
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Step 3

19. Binary to Decimal
Technique 1:
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Step 4

20. Binary to Decimal
Technique 1:
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Step 5

21. Binary to Decimal
Technique 2:
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Step 1

22. Binary to Decimal
Technique 2:
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Step 2

23. Binary to Decimal
Technique 2:
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Step 3

24. Binary to Decimal
Technique 2:
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Step 4

25. Binary to Decimal
Technique 2:
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Step 5

26. Binary to Decimal
Technique 2:
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Step 6

27. Binary to Decimal
Technique 2:
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Step 7

28. Binary to Decimal
Technique 2:
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Step 9

29. Binary to Decimal- Decimal to Binary
(123)10 =
( )2 = 227
150 =
= 162
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30. Summary of Decimal Number System
A positional Number System
Has 10 Symbols or Digits (0,1,2,3,4, 5,6,7,8 ,9).
Hence its base is 10.
The maximum value of single digit is 9.
Each position of a digit represent a specific power of the base 10.
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31. Summary of Decimal Number System
In positional number systems, there are only few symbols, called digits, and these symbols represent values, depending on the position , they occupy in the number.
The value of each digit is determined by three steps
The digit itself
The position of the digit in the number
The base of the number systems
Examples
Decimal number systems
Binary number systems
Octal number systems
Hexadecimal number systems.
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32. Summary of Binary Number System
As we know that decimal system the base is equal to 10. It means that there are 10 digits in decimal system i.e. 0,1,2,3,…,9.
Binary number system is same as decimal system, except that the base is 2, instead of 10.
In Binary System there are only two digits (0,1) , which can be used.
Each position in a binary system represent the power of base (2)
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33. Summary of Binary Number System
3/31/2017 =
= 21

34. Octal Number System In Octal Number System, the base is 8.
So, there are eight digits: 0,1,2,3,4,5,6 and 7.
Each position in an octal number represents a power of base 8.
Since there are only 8 digits, so 3 bits are sufficient to represent any octal number in binary,
Example =
= 1071

35. Hexadecimal Number System
In hexadecimal number system, the base is 16.
So, there are 16 digits or symbols in hexadecimal number system.
First 10 digits are 0,1,2,3,4,5,6,7,8,9.
The remaining six digits are denoted by the symbols A, B, C, D, E and F, representing the decimal values 10, 11,12, 13, 14 and 15, respectively.
Each position in the hexadecimal system represents a power of the base (16)
Example:
= (1 * 256) + (10 * 16) + (15 * 1) =
= 431

36. Converting From One Number System To Another
Any number in one number system can be represented in other number system.
In computer system, the input and output is mostly in decimal number system.
So, computer takes input in decimal and convert it into binary than process the input and converts again in decimal to produce output. Which is understandable to user.

37. Converting From Decimal to Another Base
Four Steps
Divide the decimal number to be converted by the value of new base.
Record the remainder from Step 1 as the right most digit of the new base number.
Divide the quotient of the previous divide by the new base.
Record the remainder from step 3 as the next digit (to the left) of the new base.
Repeat Step 3 and 4 until the quotient becomes zero.

38. Converting From Decimal To Another Base
Example
remainder
Hence =

39. Converting to Decimal from Another Base
Three steps.
Determine the column value of each digit (this depends on the position of the digit and the base of the number).
Multiply the obtain column values by the digits in the corresponding columns.
Sum the products calculated in step 2. The total is equivalent value in decimal.

40. Converting to Decimal from Another Base
Example
Step 1: Determine the values. 1 2 3 4 5
Step 2: Multiply Column values by corresponding column digits
(1x16) + (1x8) + (0x4) + (0x2) + (1x1)
Step 3: Sum the product
= 25

41. Decimal to Octal
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Step 9

42. Octal to Decimal
The given number is  = (2 * 82) + (0 * 81) + (1 * 80) = 2 * * * 1 = = 129 The equivalent decimal number for 2018 is  = 129
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43. Decimal to Octal - Octal to Decimal
The given number is (532) 10 = ( ?) 8
The given number is (532) 8 = ( ?) 10
Answer:
1024,
346
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44. Hexadecimal Numbering systems
Base: 16
Digits: 0, 1, 2, 3, 4, 5, 6, 7,8,9,A,B,C,D,E,F
Hexadecimal number: 1F416
powers of :
decimal value:
Hexadecimal number: F 4

45. Hexadecimal Numbering systems
Four-bit Group Decimal Digit Hexadecimal Digit A B C D E F

46. Hexa to Decimal Conversion
To convert to base 10, beginning with the rightmost digit
multiply each nth digit by 16(n-1), and add all of the results
together.
Ex: 1F416
positional powers of 16:
decimal positional value:
Hexadecimal number: F 4 =

47. Converting From a Base Other Than 10 to a Base Other than 10
Two Steps
Convert The original number into decimal number system
Convert the decimal number obtained in step 1 to the new number.

48. Shortcut Method of converting Binary number system to Octal Number System
Step 1: Divide the digits into group of three starting from the right
Step 2: Convert each group of three binary digits to one octal digit using the method of binary to decimal conversion.

49. Shortcut Method of converting Binary number system to Octal Number System

50. Shortcut Method of converting Octal Number System to Binary number system

51. Shortcut Method of converting Binary number system to Hexadecimal Number System
Step 1: Divide the digits into group of four starting from the right
Step 2: Convert each group of four binary digits to one Hexadecimal number.

52. Shortcut Method of converting Binary number system to Hexadecimal Number System

53. Shortcut Method of converting Hexadecimal Number System to Binary number system
Step 1: Convert Each Hexadecimal digit to a 4 digit binary number.
Step 2: Combine all the resulting binary groups into a single binary number

54. Shortcut Method of converting Hexadecimal Number System to Binary number system

55. Fractional Numbers

56. Formation of Fractional Numbers in Binary Number System

57. Anyone who has never made a mistake has never tried anything new.
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Anyone who has never made a mistake has never tried anything new.
Einstein