Question

I have a decimal fraction: 76.234567x10^-14

I need to convert this number to binary. I know you can multiply the number by 2 constantly to get the binary number, but that will take forever to do, even converting it to hex with x16 takes a long time, is there any easier way to convert this?

Show all steps and work please.

Answer 1

There is not any other way. You gotta do it manually. Once you have the binary, change 4 bits to equivalent hex which will reduce a little work.

• To binary

76.234567x10^-14 = 0.00000000000076234567

1 : 0.0 * 2 = 0.0
2 : 0.0 * 2 = 0.0
3 : 0.0 * 2 = 0.0
4 : 0.0 * 2 = 0.0
5 : 0.0 * 2 = 0.0
6 : 0.0 * 2 = 0.0
7 : 0.0 * 2 = 0.0
8 : 0.0 * 2 = 0.0
9 : 0.0 * 2 = 0.0
10 :     0.0 * 2 = 0.0
11 :     0.0 * 2 = 0.0
12 :     0.0 * 2 = 0.0
13 :     0.0 * 2 = 0.0
14 :     0.0 * 2 = 0.0
15 :     0.0 * 2 = 0.0
16 :     0.0 * 2 = 0.0
17 :     0.0 * 2 = 0.0
18 :     0.0 * 2 = 0.0
19 :     0.0 * 2 = 0.0
20 :     0.0 * 2 = 0.0
21 :     0.0 * 2 = 0.0
22 :     0.0 * 2 = 0.0
23 :     0.0 * 2 = 0.0
24 :     0.0 * 2 = 0.0
25 :     0.0 * 2 = 0.0
26 :     0.0 * 2 = 0.0
27 :     0.0 * 2 = 0.0
28 :     0.0 * 2 = 0.0
29 :     0.0 * 2 = 0.0
30 :     0.0 * 2 = 0.0
31 :     0.0 * 2 = 0.0
32 :     0.0 * 2 = 0.0
33 :     0.0 * 2 = 0.01
34 :     0.01 * 2 = 0.01
35 :     0.01 * 2 = 0.03
36 :     0.03 * 2 = 0.05
37 :     0.05 * 2 = 0.1
38 :     0.1 * 2 = 0.21
39 :     0.21 * 2 = 0.42
40 :     0.42 * 2 = 0.84
41 :     0.84 * 2 = 1.68
42 :     0.68 * 2 = 1.35
43 :     0.35 * 2 = 0.71
44 :     0.71 * 2 = 1.41
45 :     0.41 * 2 = 0.82
46 :     0.82 * 2 = 1.65
47 :     0.65 * 2 = 1.29
48 :     0.29 * 2 = 0.58
49 :     0.58 * 2 = 1.16
50 :     0.16 * 2 = 0.32
51 :     0.32 * 2 = 0.65
52 :     0.65 * 2 = 1.3
53 :     0.3 * 2 = 0.6
54 :     0.6 * 2 = 1.2
55 :     0.2 * 2 = 0.4
56 :     0.4 * 2 = 0.79
57 :     0.79 * 2 = 1.59
58 :     0.59 * 2 = 1.18
59 :     0.18 * 2 = 0.36
60 :     0.36 * 2 = 0.72
61 :     0.72 * 2 = 1.43
62 :     0.43 * 2 = 0.87
63 :     0.87 * 2 = 1.74
64 :     0.74 * 2 = 1.47
65 :     0.47 * 2 = 0.94
66 :     0.94 * 2 = 1.88
67 :     0.88 * 2 = 1.76
68 :     0.76 * 2 = 1.52
69 :     0.52 * 2 = 1.05
70 :     0.05 * 2 = 0.09
71 :     0.09 * 2 = 0.18
72 :     0.18 * 2 = 0.37
73 :     0.37 * 2 = 0.74
74 :     0.74 * 2 = 1.48
75 :     0.48 * 2 = 0.95
76 :     0.95 * 2 = 1.9
77 :     0.9 * 2 = 1.8
78 :     0.8 * 2 = 1.6
79 :     0.6 * 2 = 1.21
80 :     0.21 * 2 = 0.41
81 :     0.41 * 2 = 0.83
82 :     0.83 * 2 = 1.65
83 :     0.65 * 2 = 1.31
84 :     0.31 * 2 = 0.62
85 :     0.62 * 2 = 1.23
86 :     0.23 * 2 = 0.47
87 :     0.47 * 2 = 0.94
88 :     0.94 * 2 = 1.88
89 :     0.88 * 2 = 1.75
90 :     0.75 * 2 = 1.5
91 :     0.5 * 2 = 1.0
Answer: 0. 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1101 0110 1001 0100 1100 1011 0111 1000 0101 1110 0110 1001 111

• To Hex: Once you have the binary, change 4 bits to equivalent hex

0.0000 0000 00D6 94CB 785E 69E

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