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M1.2B ALGEBRA > BINARY AND OTHER NUMBERING SYSTEMS > Flashcards

BINARY AND OTHER NUMBERING SYSTEMS Flashcards

1
Q

WHAT ARE EVERYDAY NUMBERS IN?

A

BASE 10

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2
Q

HOW DO YOU COUNT UP TO THE NUMBER NINETY-NINE?

A

BY REPEATEDLY ADDING ONE TO THE UNITS COLUMN UNTIL NINE IS REACHED.
THEN BEGIN AT ZERO AGAIN
ADDING ONE TO THE TENS COLUMN

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3
Q

NUMBERING SYSTEMS

WHAT IS BINARYS BASE?

A

2

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4
Q

NUMBERING SYSTEMS

WHAT ARE BINARYS DIGITS?

A

0,1

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5
Q

NUMBERING SYSTEMS

WHAT IS OCTALS BASE?

A

8

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6
Q

NUMBERING SYSTEMS

WHAT ARE OCTALS DIGITS?

A

0,1,2,3,4,5,6,7

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7
Q

NUMBERING SYSTEMS

WHAT IS DECIMALS BASE?

A

10?

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8
Q

NUMBERING SYSTEMS

WHAT ARE DECIMALS DIGITS?

A

0,1,2,3,4,5,6,7,8,9

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9
Q

NUMBERING SYSTEMS

WHAT IS HEXADECIMALS BASE?

A

16

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10
Q

NUMBERING SYSTEMS

WHAT ARE HEXADECIMALS DIGITS?

A

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

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11
Q

BINARY

WHAT IS BINARY?

A

A NUMBER SYSTEM THAT ONLY USES TWO DIGITS
1 AND 2

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12
Q

BINARY

WHAT IS BINARY BASED ON?

A

SWITCHES AND VALVES THAT HAVE TWO STATES
ON AND OFF
OPEN OR CLOSED

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13
Q

BINARY

HOW IS COMPUTER INFORMATION PROCESSED?

A

INFORMATION PROCESSED BY A COMPUTER IS IN THE FORM OF A SEQUENCE OF ONES AND ZEROS.

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14
Q

BINARY

WHAT MUST WE DO FOR INFORMATION THAT IS TO BE PROCESSED BY A COMPUTER?

A

CONVERT ALL DATA INTO BINARY

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15
Q

BINARY PLACE VALUES

2^7

A

128

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16
Q

BINARY PLACE VALUES

2^6

A

64

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17
Q

BINARY PLACE VALUES

2^5

A

32

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18
Q

BINARY PLACE VALUES

2^4

A

16

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19
Q

BINARY PLACE VALUES

2^3

A

8

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20
Q

BINARY PLACE VALUES

2^2

A

4

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21
Q

BINARY PLACE VALUES

2^1

A

2

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22
Q

BINARY PLACE VALUES

2^0

A

1

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23
Q

BINARY PLACE VALUES

2^-1

A

0.5

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24
Q

BINARY PLACE VALUES

2^-2

A

0.25

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25
Q

OCTAL

WHAT DOES BASE 8 MEAN?

A

THE SYSTEM ONLY USES 8 DIGITS FROM
0-7

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26
Q

OCTAL

WHAT IS IMPORTANT TO NOTE ABOUT THE PHYSICAL MEANING OF OCTAL NUMBERS?

A

THAT THE NUMBERS FROM 0-7 HAVE THE SAME PHYSICAL MEANING AS THAT OF DECIMAL NUMBERS

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27
Q

OCTAL

WHAT IS OCTAL USED BY?

A

OCTAL IS ANOTHER SYSTEM USED BY COMPUTERS WHEN THEY SENF INFORMATION.

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28
Q

OCTAL PLACE VALUES

8^7

A

2, 097, 152

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29
Q

OCTAL PLACE VALUES

8^6

A

262, 144

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30
Q

OCTAL PLACE VALUES

8^5

A

32, 768

31
Q

OCTAL PLACE VALUES

8^4

A

4, 096

32
Q

OCTAL PLACE VALUES

8^3

A

512

33
Q

OCTAL PLACE VALUES

8^2

A

64

34
Q

OCTAL PLACE VALUES

8^1

A

8

35
Q

OCTAL PLACE VALUES

8^0

A

1

36
Q

OCTAL

HOW TO WORK OUT AN OCTAL NUMBER

A
  1. 237₈
  2. 2 x 8 ² = 128 (TWO FROM THE HUNDREDS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 2)
    • 3 x 8 ¹ = 28 (THREE FROM THE TENS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 1)
    • 7 x 8⁰ = 7 (SEVEN FROM THE UNITS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 0)
  5. 128 + 24 + 7 = 159₁₀ (SUBSCRIPT 10 AS IT IS NOW IN A BASE 10 DECIMAL
37
Q

HEXADECIMAL

WHAT IS HEXADECIMAL?

A

HEXADECIMAL IS A BASE 16 NUMBERING SYSTEM.

38
Q

HEXADECIMAL

WHAT IS THE HEXADECIMAL SYSTEM MADE UP OF?

A
  • 16 DIGITS
  • 0-9
  • AND LETTERS
  • A-F
39
Q

HEXADECIMAL

WHY DOES THE HEXADECIMAL SYSTEM USE LETTERS?

A
  • THE TEN DIGITS USED IN THE DECIMAL SYSTEM ARE NOT SUFFICIENT
  • LETTERS ARE USED TO REPRESENT THE VALUES
  • 10,11,12,13,14,15
40
Q

WHAT DOES ₁₀ MEAN?

A

DECIMAL

41
Q

WHAT DOES ₈ MEAN?

A

OCTAL

42
Q

WHAT DOES ₁₆ MEAN?

A

HEXADECIMAL

43
Q

WHAT DOES ₂ MEAN?

A

BINARY

44
Q

WHAT ARE THE 4 NUMBERING SYSTEMS?

A
  • BINARY
  • OCTAL
  • DECIMAL
  • HEXADECIMAL
45
Q

HEXADECIMAL PLACE VALUES

0

A

0

46
Q

HEXADECIMAL PLACE VALUES

1

A

1

47
Q

HEXADECIMAL PLACE VALUES

2

A

2

48
Q

HEXADECIMAL PLACE VALUES

3

A

3

49
Q

HEXADECIMAL PLACE VALUES

4

A

4

50
Q

HEXADECIMAL PLACE VALUES

5

A

5

51
Q

HEXADECIMAL PLACE VALUES

6

A

6

52
Q

HEXADECIMAL PLACE VALUES

7

A

7

53
Q

HEXADECIMAL PLACE VALUES

8

A

8

54
Q

HEXADECIMAL PLACE VALUES

9

A

9

55
Q

HEXADECIMAL PLACE VALUES

10

A

A

56
Q

HEXADECIMAL PLACE VALUES

11

A

B

57
Q

HEXADECIMAL PLACE VALUES

12

A

C

58
Q

HEXADECIMAL PLACE VALUES

13

A

D

59
Q

HEXADECIMAL PLACE VALUES

14

A

E

60
Q

HEXADECIMAL PLACE VALUES

15

A

F

61
Q

HEXADECIMAL

WHEN IS HEXADECIMAL NUMBERING SYSTEM USED?

A

BY PROGRAMMERS TO SIMPLIFY THE BINARY NUMBERING SYSTEM

62
Q

HEXADECIMAL

HOW IS 16 EQUIVALENT TO 2⁴?

A
  • 2√16=4
  • 4 X 4 = 16
  • THERE IS A LINEAR RELATIONSHIP BETWEEN 2 AND 16
63
Q

HEXADECIMAL

WHAT IS THE RELATION BETWEEN HEXADECIMAL AND BINARY?

A
  • EACH PLACE IN A HEXADECIMAL NUMBER REPRESENTS UP TO FOUR PLACES IN A BINARY NUMBER
  • THE BINARY NUMBERS 0 - 1111 ARE REPRESENTED BY 0 TO F
64
Q

HEXADECIMAL

WHAT PROGRAMMES ARE HEXADECIMAL USED IN?

A
  • COLOUR REFERENCES
  • ASSEMBLY LANGUAGE PROGRAMMES
  • ERROR MESSAGES
65
Q

HEXADECIMAL PLACE VALUES

16⁷

A

268, 435, 456

66
Q

HEXADECIMAL PLACE VALUES

16⁶

A

16 777 216

67
Q

HEXADECIMAL PLACE VALUES

16⁵

A

1 048 576

68
Q

HEXADECIMAL PLACE VALUES

16⁴

A

65 536

69
Q

HEXADECIMAL PLACE VALUES

16³

A

4096

70
Q

HEXADECIMAL PLACE VALUES

16²

A

256

71
Q

HEXADECIMAL PLACE VALUES

16¹

A

16

72
Q

HEXADECIMAL PLACE VALUES

16⁰

A

1

73
Q

HEXADECIMAL

HEXADECIMAL IS A PLACE VALUE SYSTEM; WHAT DOES THAT MEAN?

A
  • EACH PLACE REPRESENTS A POWER OF 16
  • THE PLACE REPRESENTS A POWER OF 10 IN THE DECIMAL SYSTEM

M1.2B ALGEBRA (6 decks)

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