Hello All!I want an algorithm to convert the given number in given base to other base?

Question

For ex:
101 base 4 = ? base 26
The condition is that i have to do it directly..that is conversion via binary or decimal conversion is not allowed

Answer 1

101 b4 = (1+0*4+1*4^2)b26 = Hb26

I don't see how you can do this directly without converting since our brain are wired to operate in base 10 and our computers wired to operate in base 2. I mean either way you need to compute the quantity involved in one base and convert.

Or you could figure out how much the larger base is in the smaller base: 26 = 16 + 8 + 2 = 122b4 and subtract that number successively from the number to convert until you get a number smaller than 26, where you need a lookup table to complete the job. Each time you subtract you have to has 10 to the result.

Answer 2

101 base 4 = ? base 26

Strange question

101 base 4= 1*4^2+0*4^1+1*4^0 =17

17 base 26 = q (assuming we use the letters of the alphabet to obtain fillin the digits in base 26, q is the 17th letter)


For your algorithm you specify that you cannot convert via another base.

Let abc be a three digit number base d. We want to find its equivalent in base g


Example

345 base 6 = ? base 4

36= 210 base 4 (2*16+4 base 10 for comparison)
6= 12 base 4

So we have 3 * 36 base 6 = 3*210 base 4= 1230 base 4
4* 6 base 6 = 4*12 =120 base 4
5 =11 base 4

add 1230+
120
11
= 2 0 2 1 base 4
checking 345 base 6 is3*36+4*6+5 = 137 base 10

2* 64+2*4+1 =128+8+1=137 base 10


Cheers

Answer 3

I am afraid the only way is to convert 26 in base 4. Then divide in base 4 to get A = 26 B +C where C is the remainder will be the unit.
Then you do it with B and so on and you get in base 4 the numbers of the development in base 26. Finally it's easy to translate those.

In your example there is not much because 101 in base 4 is just 17.
So lets take 3333. 26 is 122 in base 4.
To get started it's better to get a feeling of the multiples 122
310, 1032, 1220, etc so 3100 is 20 x 122 and 3222 = 21x122.
So 3333 = 21x122 + 111. And since 21 and 111<122 that's it
(3333)_4= (21,111)_26=(9,21)_26.

A good mental exercise...

Answer 4

101 base 4 = 1X4^2 + 0X4^1 1X4^0 =16+1(base 10)=17

Let's see if I can explain this properly. You'll need to remember your powers of the base, so for the number 1000 in base 10 it would be
0 X 10^ 0 0X10^1 0X10^2 1X10^3 if you wanted 6000 it would be 6X10^3. Your number places begin from the right and move leftward increasing the exponent by one.
10^3 10^2 10^1 10^0
1 . . . . 0 . . 0 . . . 0

So for base 26

26^2 26^1 26^0
0 . . . . 0 . . 17(you'll need a character to represent this)



So 101(base 4) = 17(base 10) =
If you use the alphabet then it could be represented as Q if you use 10 numbers followed by letters it would be G.
You need a single character to represent the double character numbers though

Answer 5

divide 101 by 26 and place the quotient in tens place and the remainder in ones place
in this case the ones place is 23
you can represent the numbers above 9 by letters
if we start representing 10 by a
the the number will be 3m

Answer 6

164.125