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Programming Precepts > Number Bases Equations. > Flashcards

Number Bases Equations. Flashcards

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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
BEDMAS | -3^2 =
9
26
SCIENTIFIC NOTATION: | 93000000
9.3 x 10^3
27
SCIENTIFIC NOTATION: | 14.689
1.4689 x 10^1
28
SCIENTIFIC NOTATION: | -0.003164
-3.164 x 10^-3
29
SCIENTIFIC NOTATION: | -6381.765
-6.381765 x 10^3
30
NORMALIZED EXPONENTIAL FORMAT: | 93000000
0.93 x 10^8
31
NORMALIZED EXPONENTIAL FORMAT: | 10111.011
.10111011 x 2^5
32
NORMALIZED EXPONENTIAL FORMAT: | 0.000257
0.257 x 8^-3
33
NORMALIZED EXPONENTIAL FORMAT: | -6381.765
-0.6381765 x 10^4
34
Write the number 21.78 in its expanded notation...?
2x10^1 + 1x10^0 + 7x10^-1 + 8x10^-2
35
Write the number 3/8 in its expanded decimal notation...?
``` 3/8 = 0.375 Answer = 3x10^-1 + 7x10^-2 + 5x10^-3 ```
36
find the decimal equivalent of the binary numbers (a) 1011.011 and (b) 10.101
a) = 11.375 | b) = 2.625
37
Convert the number 115 to binary form using the Algorithm method.
= 1110011 | check by expanding.
38
Convert the number 149 to binary
= 10010101
39
Convert the number 509 to binary
= 111111101
40
Convert the number 0.828125 to binary
= 0.110101
41
Convert the number 12.3125 to binary
= 110.0101
42
Convert the number 0.3 to binary
= 0.0|1001|
43
Convert 4126 (Octal) to Decimal
= 2134
44
Convert 35.14 (Octal) to Decimal
= 29.1875
45
Convert 315 to Octal
= 473
46
Convert 0.34375 to Octal
= 0.26
47
Convert 142.15625 to Octal
= 216.12
48
Convert 1101110 to Octal (using a 3 bit , not a 4 bit like in hexadecimal)
=156.
49
Convert 3146 (Octal) to Binary
= 11001100010110
50
Convert B37 (Hexadecimal) to Decimal
= 2871
51
Convert 421 (Hexadecimal) to Decimal
= 1A5
52
Convert 110010111001011001101101 to Hexadecimal using the (4 bit table)
= CB966D
53
Convert 101101010000110110 to Hexadecimal
= 2D436
54
Convert A2E47 to binary
= 10100010111001000111
55
Convert 1D7 to binary
= 11010111
56
Binary 10 + 10 =
= 100
57
Binary 10 + 10 + 10 =
= 110
58
Binary 10 + 10 + 10 + 10 =
= 1000
59
Binary 101 + 100 =
= 1001
60
Binary 111 + 100 + 11 =
= 1110
61
Binary 101 - 10 =
= 11
62
Binary 111 - 11 =
= 100
63
Binary 100 - 11 =
= 1 (check by adding the answer and the number taken away together)
64
Binary 1000 - 1101 =
= 11
65
Find the Complement of (a) 1101 and (b) 10101
a) = 0011 b) = 1011
66
Binary 100011 - 1010 =
= 11001 (Read the PDF if you dont remember this)
67
Binary 10110 - 1101 =
= 1001
68
Find the One and twos complement of (a) 1011010, (b) 11011101 and (c) 111011111
a) = 100101 and 100110 b) = 100010 and 100011 c) = 100000 and 100001
69
Write 3482 in Expanded Decimal notation.
3x10^3 + 4x10^2 + 8x10^1 + 2x10^0
70
Write 44.2875 in expanded Decimal notation.
4x10^1 + 4x10^0 + 2x10^-1 + 8x10^-2 + 7x10^-3 + 5x10^-4
71
Write the binary number 110.1001 in expanded binary notation.
= 1x2^2 + 1x2^1 + 0x2^0 + 1x2^-1 + 0x2^-2 + 0x2^-3 + 1x2^-4
72
Convert 110.1001 to decimal
6.5625
73
Convert 173 to binary
10101101
74
Convert 0.734375 to binary
= 0.101111
75
Convert 0.85 to binary
= 0.11|0110|
76
Convert 425 to Binary
=110101001
77
Convert 28 to Binary
= 11100
78
Convert the octal number 4647132 to decimal
= 1265242
79
Convert 214.078125 to base 8
=326.05
80
Convert the number 100110100111001011010 to (a) octal and (b) hexadecimal representation.
a) = 4647132 | b) = 134E5A
81
Convert the octal number 4613 to binary
= 100110001011
82
Convert the hexadecimal value 134E5A to decimal
= 1265242
83
Convert the hexadecimal number 8D2B to octal representation
``` Binary = 1000110100101011 Octal = 106453 ```
84
Convert these rational numbers to a terminating or repeating decimal: (a) 5/2 (b) 1/12, (c) 3/11 and (d) 4/7
a) = 2.5 b) = 0.8|3| c) = 0.|27| d) = 0.|571428|
85
Convert these binary numbers to decimal representation: (a) 10111.01, (b) 111111.1 (c) 100000000
a) = 23.25 b) = 63.5 c) = 256
86
Convert these Decimal numbers to binary, looking for repeating patterns. (a) 3.6 (b) 0.55 (c) 4.4
a) = 11.|1001| b) = 0.|10001| (Could be an error here) c) = 100.|0110|
87
Convert each of these octal values to binary: (a)47 (b)526 (c) 3105
a) =100111 b) = 101010110 c) = 11001000101
88
Convert these binary values to octal: (a) 1001101 (b) 101.101 (c)100100101011
a) = 115 b) = 5.5 c) = 4453
89
Convert each hexadecimal number to binary; then convert the result to decimal. (a) AB, (b) E4D, (c) 3F6
a) = 171 b) = 3661 c) = 1014
90
Perform the following operations in binary; check your result by converting everything to decimal: (a) 1010 + 0110 (b) 11010 + 1101, (c) 11010 - 1101
a) = 10000 b) = 100111 c) = 1101

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