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Programming Precepts > Number Bases Equations. > Flashcards

Number Bases Equations. Flashcards

1
Q

Expanded decimal notation:

356.12 =

A

3x10^2 + 5x10^1 + 6x10^0 + 1x10^-1 + 2x10^-2

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2
Q

Expanded Binary Notation:

101.01 =

A

1x2^2 + 0x2^1 + 1x2^0 + 0x2^-1 + 1x2^-2

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3
Q

Decimal to Binary:

315 =

A

100111011

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4
Q

Decimal to Binary:

0.625 =

A

0.101

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5
Q

Decimal to Binary:

104.15625 =

A

1101000.00101

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6
Q

Decimal to Binary:

19.1 =

A

10011.0|0011| repeating bars.

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7
Q

Hexadecimal to Decimal:

E5B.F2 =

A

Ex16^2 + 5x16^1 + Bx16^0 + Fx16^-1 + 2x16^-2

14x16^2 + 5x16^1 + 11x16^0 + 15x16^-1 + 2x16^-2

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8
Q

Binary to Hexadecimal:

1100101100011101010 =

A

(Divide this up into groups of four starting on the right, and make a 4-bit binary table)
= 658EA

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9
Q

Binary to Hexadecimal:

101110101101.0001111

A

= BAD.1E

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10
Q

Hexadecimal to Binary:

3C.A29 =

A

(Like in Binary to Hexadecimal use the 4-bit binary table)

111100.101000101001

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11
Q

Find the One and Twos complement….?

1110

A

0001

0010 (Remember to carry the 1)

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12
Q

Find the One and Twos complement…?

11100

A

00011

00100

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13
Q

Addition of Binary Numbers…?

10011 + 11001

A

= 101100

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14
Q

Addition of Binary Numbers…?

10111 + 11011

A

= 110010

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15
Q

Addition of Binary Numbers…?

110111 + 1110

A

= 1010101

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16
Q

Subtraction of Binary Numbers…?

10110 - 1101

A

= (See PDFs)

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17
Q

Subtraction of Binary Numbers…?

100101 - 101110

A

= (See PDFs)

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18
Q

Subtraction of Binary Numbers…?

110 - 110101

A

= (See PDFs)

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19
Q

Modulo

A

(Look at tables in book from page 28 to page 29 still learning)

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20
Q

Write an algorithm to convert a decimal number between 0 and 1 to binary…?

A 
first step Input the number
2
3
4
5
6
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21
Q

Draw a structure diagram for an algorithm for converting a decimal number between 0 and 1 to binary…?

A

(do it)

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22
Q

BEDMAS

12+3x4 =

A

24

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23
Q

BEDMAS

-2^4 / 8 * 5 =

A

10

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24
Q

BEDMAS

4 * (-3^2) / (2 * 5^-1) + 6 * (2 * 4^-2) =

A

90 3/4

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25
Q

BEDMAS

-3^2 =

A

9

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26
Q

SCIENTIFIC NOTATION:

93000000

A

9.3 x 10^3

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27
Q

SCIENTIFIC NOTATION:

14.689

A

1.4689 x 10^1

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28
Q

SCIENTIFIC NOTATION:

-0.003164

A

-3.164 x 10^-3

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29
Q

SCIENTIFIC NOTATION:

-6381.765

A

-6.381765 x 10^3

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30
Q

NORMALIZED EXPONENTIAL FORMAT:

93000000

A

0.93 x 10^8

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31
Q

NORMALIZED EXPONENTIAL FORMAT:

10111.011

A

.10111011 x 2^5

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32
Q

NORMALIZED EXPONENTIAL FORMAT:

0.000257

A

0.257 x 8^-3

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33
Q

NORMALIZED EXPONENTIAL FORMAT:

-6381.765

A

-0.6381765 x 10^4

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34
Q

Write the number 21.78 in its expanded notation…?

A

2x10^1 + 1x10^0 + 7x10^-1 + 8x10^-2

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35
Q

Write the number 3/8 in its expanded decimal notation…?

A 
3/8 = 0.375
Answer = 3x10^-1 + 7x10^-2 + 5x10^-3
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36
Q

find the decimal equivalent of the binary numbers (a) 1011.011 and (b) 10.101

A

a) = 11.375

b) = 2.625

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37
Q

Convert the number 115 to binary form using the Algorithm method.

A

= 1110011

check by expanding.

38
Q

Convert the number 149 to binary

A

= 10010101

39
Q

Convert the number 509 to binary

A

= 111111101

40
Q

Convert the number 0.828125 to binary

A

= 0.110101

41
Q

Convert the number 12.3125 to binary

A

= 110.0101

42
Q

Convert the number 0.3 to binary

A

= 0.0|1001|

43
Q

Convert 4126 (Octal) to Decimal

A

= 2134

44
Q

Convert 35.14 (Octal) to Decimal

A

= 29.1875

45
Q

Convert 315 to Octal

A

= 473

46
Q

Convert 0.34375 to Octal

A

= 0.26

47
Q

Convert 142.15625 to Octal

A

= 216.12

48
Q

Convert 1101110 to Octal (using a 3 bit , not a 4 bit like in hexadecimal)

A

=156.

49
Q

Convert 3146 (Octal) to Binary

A

= 11001100010110

50
Q

Convert B37 (Hexadecimal) to Decimal

A

= 2871

51
Q

Convert 421 (Hexadecimal) to Decimal

A

= 1A5

52
Q

Convert 110010111001011001101101 to Hexadecimal using the (4 bit table)

A

= CB966D

53
Q

Convert 101101010000110110 to Hexadecimal

A

= 2D436

54
Q

Convert A2E47 to binary

A

= 10100010111001000111

55
Q

Convert 1D7 to binary

A

= 11010111

56
Q

Binary 10 + 10 =

A

= 100

57
Q

Binary 10 + 10 + 10 =

A

= 110

58
Q

Binary 10 + 10 + 10 + 10 =

A

= 1000

59
Q

Binary 101 + 100 =

A

= 1001

60
Q

Binary 111 + 100 + 11 =

A

= 1110

61
Q

Binary 101 - 10 =

A

= 11

62
Q

Binary 111 - 11 =

A

= 100

63
Q

Binary 100 - 11 =

A

= 1 (check by adding the answer and the number taken away together)

64
Q

Binary 1000 - 1101 =

A

= 11

65
Q

Find the Complement of (a) 1101 and (b) 10101

A

a) = 0011 b) = 1011

66
Q

Binary 100011 - 1010 =

A

= 11001 (Read the PDF if you dont remember this)

67
Q

Binary 10110 - 1101 =

A

= 1001

68
Q

Find the One and twos complement of (a) 1011010, (b) 11011101 and (c) 111011111

A

a) = 100101 and 100110
b) = 100010 and 100011
c) = 100000 and 100001

69
Q

Write 3482 in Expanded Decimal notation.

A

3x10^3 + 4x10^2 + 8x10^1 + 2x10^0

70
Q

Write 44.2875 in expanded Decimal notation.

A

4x10^1 + 4x10^0 + 2x10^-1 + 8x10^-2 + 7x10^-3 + 5x10^-4

71
Q

Write the binary number 110.1001 in expanded binary notation.

A

= 1x2^2 + 1x2^1 + 0x2^0 + 1x2^-1 + 0x2^-2 + 0x2^-3 + 1x2^-4

72
Q

Convert 110.1001 to decimal

A

6.5625

73
Q

Convert 173 to binary

A

10101101

74
Q

Convert 0.734375 to binary

A

= 0.101111

75
Q

Convert 0.85 to binary

A

= 0.11|0110|

76
Q

Convert 425 to Binary

A

=110101001

77
Q

Convert 28 to Binary

A

= 11100

78
Q

Convert the octal number 4647132 to decimal

A

= 1265242

79
Q

Convert 214.078125 to base 8

A

=326.05

80
Q

Convert the number 100110100111001011010 to (a) octal and (b) hexadecimal representation.

A

a) = 4647132

b) = 134E5A

81
Q

Convert the octal number 4613 to binary

A

= 100110001011

82
Q

Convert the hexadecimal value 134E5A to decimal

A

= 1265242

83
Q

Convert the hexadecimal number 8D2B to octal representation

A 
Binary = 1000110100101011
Octal = 106453
84
Q

Convert these rational numbers to a terminating or repeating decimal: (a) 5/2 (b) 1/12, (c) 3/11 and (d) 4/7

A

a) = 2.5
b) = 0.8|3|
c) = 0.|27|
d) = 0.|571428|

85
Q

Convert these binary numbers to decimal representation: (a) 10111.01, (b) 111111.1 (c) 100000000

A

a) = 23.25
b) = 63.5
c) = 256

86
Q

Convert these Decimal numbers to binary, looking for repeating patterns. (a) 3.6 (b) 0.55 (c) 4.4

A

a) = 11.|1001|
b) = 0.|10001| (Could be an error here)
c) = 100.|0110|

87
Q

Convert each of these octal values to binary: (a)47 (b)526 (c) 3105

A

a) =100111
b) = 101010110
c) = 11001000101

88
Q

Convert these binary values to octal: (a) 1001101 (b) 101.101 (c)100100101011

A

a) = 115
b) = 5.5
c) = 4453

89
Q

Convert each hexadecimal number to binary; then convert the result to decimal.
(a) AB, (b) E4D, (c) 3F6

A

a) = 171
b) = 3661
c) = 1014

90
Q

Perform the following operations in binary; check your result by converting everything to decimal: (a) 1010 + 0110 (b) 11010 + 1101, (c) 11010 - 1101

A

a) = 10000
b) = 100111
c) = 1101

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