2. The Context of Cybersecurity: Cyberspace 13 Table 2.3 Ten binary places are approximately equal to three decimal places. As an example, if we wanted to assign every human being their own unique binary string, how many bits would we need? The population of Earth is around eight billion people: 8,000,000,000 = 8 x 109 This number can be converted to a power of two by first converting eight to a power of two: 8 = 23 (Note: when using this rule, it does not always work out for the power of two to equal the leading digits—that is fine because this is just an approximation anyway. In that case, just go with the nearest power of two.) Then 109 can be converted to a power of two by converting the three groups of three decimal places (9 ÷ 3 = 3) to three groups of ten binary places (3 x 10 = 30): 109 ≈ 230 The final approximation is: 23 x 230 = 233 = 8,589,934,592 The quick approximation yields the same order of magnitude and is close enough to the actual number for most purposes. This calculation shows that we would need thirty-three bits to assign every person a unique binary string. If we wanted to be on the safe side for the foreseeable future, we could add another bit which would double the number of possibilities to over seventeen billion—that many should hold up for quite a while! Using the base two-base ten conversion rule, we can also go the other way from powers of two to powers of ten. Earlier we said we would need sixty-three bits to encode every grain of sand on Earth. To get a better idea of how big of a number this is, we can convert it to a power of ten. To isolate the groups of ten zeros we can write 263 as:
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