StackOverflow2013

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PO
primarykey
Id
12577910
data
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0
AnswerCount
0
ClosedDate
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CommunityOwnedDate
CreationDate
2012-09-25T07:11:59.190
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2012-10-01T01:18:13.140
LastEditDate
2012-10-01T01:18:13.140
LastEditorUserId
419
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1696418
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12577314
PostTypeId
2
Score
5
ViewCount
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LastEditorDisplayName
text
Body
Every base has a purpose. Usually we do base conversion to make complex computations simpler. Here are some most popular bases used and their representation. <ul> <li>2-binary numeral system used internally by nearly all computers, is base two. The two digits are <code>0</code> and <code>1</code>, expressed from switches displaying OFF and ON respectively.</li> <li>8-octal system is occasionally used in computing. The eight digits are <code>0–7</code>.</li> <li>10-decimal system the most used system of numbers in the world, is used in arithmetic. Its ten digits are <code>0–9</code>.</li> <li>12-duodecimal (dozenal) system is often used due to divisibility by 2, 3, 4 and 6. It was traditionally used as part of quantities expressed in dozens and grosses.</li> <li>16-hexadecimal system is often used in computing. The sixteen digits are <code>0–9</code> followed by <code>A–F</code>.</li> <li>60-sexagesimal system originated in ancient Sumeria and passed to the Babylonians. It is still used as the basis of our modern circular coordinate system (degrees, minutes, and seconds) and time measuring (minutes and hours).</li> <li>64-Base 64 is also occasionally used in computing, using as digits <code>A–Z,</code> <code>a–z,</code> <code>0–9</code>, plus two more characters, often <code>+</code> and <code>/</code>.</li> <li>256-bytes is used internally by computers, actually grouping eight binary digits together. For reading by humans, bytes are usually shown in hexadecimal.</li> </ul> The octal, hexadecimal and base-64 systems are often used in computing because of their ease as shorthand for binary. For example, every hexadecimal digit has an equivalent 4 digit binary number. Radices are usually natural numbers. However, other positional systems are possible, e.g. golden ratio base (whose radix is a non-integer algebraic number), and negative base (whose radix is negative). <hr> Your doubt is whether we can convert any base to any other base after base exceeds 36 ( # of Alphabets + # of digits = 26+ 10= 36) Taking example of 64-Base It uses A–Z(Upper case)(26), a–z(lower case)(26), 0–9(10), plus 2 more characters. This way the constraint of 36 is resolved. As we have (26+26+10+2)64 symbols in 64-base for representation, we can represent any number in 64 base. Similarly for more base they use different symbols for representation. Source: <a href="http://en.wikipedia.org/wiki/Radix" rel="nofollow">http://en.wikipedia.org/wiki/Radix</a>
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1. POIs it possible to convert any base to any base (range 2 to 46)
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