For example, base 3 to base 7.
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answers:
Theresa say: the only bases i know of aNot sure what to say about this
base 2 (binary)
base 8 (octal)
base 16 (hexadecimal)
and of course base 10...
i've never heard of base 3 or base 7...
in case you don't know, here are the conversations for hexadecimal from base 10...
1 = 1
2 = 2
3 = 3
this continues up to 9...
9 = 9
now things change...
10 = a
11 = b
12 = c
13 = d
14 = e
15 = f
keep in mind that base 16 (hexadecimal) means digits from 0 to f (15) which is 16 digits in total... the same way that base 10 means digits 0 - 9...
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Sqdancefan say: Use the expanded form of the base-3 number and do the arithmetic in base 7.
Base 3 . . . base 7
1 . . . . . . . . 1
2 . . . . . . . . 2
10 . . . . . . . 3
20 . . . . . . . 6
100 . . . . . . 12
200 . . . . . . 24
1000 . . . . . 36
2000 . . . . . 105
10000 . . . . 144
20000 . . . . 321
100000 . . . 465
200000 . . . 1263
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Gary B say: SURE.
But youi do int BY MEMORY, not by formula
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Dixon say: The only reason we pass through base ten is that we need to do the actual working out in a base we understand and in which we are competent. The issue is that as a human being with a Western cultural upbringing, the only base that you can reliably do arithmetic in is base ten.
If you knew your multiplication tables and paired integer sums in base 7 then you could go between base 3 and base 7 with the same ease as you currently switch between 3 and ten, and by following essentially the same method.
As noted by other answers, bases that are related by integer powers such as 2, 8, and 16 can be converted without passing through base ten because there is a one-to-one mapping of digit patterns.
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