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Base 13, for the Hitchhikker's crowd

Tuesday, December 9, 2003

Couldn't resist the call of math...

For those who were wondering, 'base n' just means that you have n symbols that represent digits. We all know what to do when you run out of symbols already - you just move over a place and start over (ie after 9 come 10). So, in base 2, for instance, that means you have '0' and '1' So, counting up from zero, you would represent the counting numbers as follows

0,1,10,11,100,101,110,111,1000,...

In base 13, we would need 13 symbols, rather than the 10 we currently have, so, lets say our set is 0,1,2,3,4,5,6,7,8,9,#,$,*

then counting up from zero, we would have

0,1,2,3,4,5,6,7,8,9,#,$,*,10,11,12,13,14,15,16,17,18,19,1#,1$,1*,20,21,22,23,24,25,26,27,28,29,2#,2$,2*,...

So, 6*9, also known as 'the question'. To get 'the answer', we need to know how to write the number that in base 10 we write as '54' in base 13. Well, we can get all the way to * before we have to move places, so that means that base 13 symbol '10' = our 13, '20'=26, '30'=39, '40'=52, '41'=53, and (ta da!) '42'=54. Woo hoo!

For those who were wondering, 'base n' just means that you have n symbols that represent digits. We all know what to do when you run out of symbols already - you just move over a place and start over (ie after 9 come 10). So, in base 2, for instance, that means you have '0' and '1' So, counting up from zero, you would represent the counting numbers as follows

0,1,10,11,100,101,110,111,1000,...

In base 13, we would need 13 symbols, rather than the 10 we currently have, so, lets say our set is 0,1,2,3,4,5,6,7,8,9,#,$,*

then counting up from zero, we would have

0,1,2,3,4,5,6,7,8,9,#,$,*,10,11,12,13,14,15,16,17,18,19,1#,1$,1*,20,21,22,23,24,25,26,27,28,29,2#,2$,2*,...

So, 6*9, also known as 'the question'. To get 'the answer', we need to know how to write the number that in base 10 we write as '54' in base 13. Well, we can get all the way to * before we have to move places, so that means that base 13 symbol '10' = our 13, '20'=26, '30'=39, '40'=52, '41'=53, and (ta da!) '42'=54. Woo hoo!

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