Published at Jul 13 2018
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Instructions

Test suite

Solution

Convert a number, represented as a sequence of digits in one base, to any other base.

Implement general base conversion. Given a number in base **a**,
represented as a sequence of digits, convert it to base **b**.

- Try to implement the conversion yourself. Do not use something else to perform the conversion for you.

In positional notation, a number in base **b** can be understood as a linear
combination of powers of **b**.

The number 42, *in base 10*, means:

(4 * 10^1) + (2 * 10^0)

The number 101010, *in base 2*, means:

(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)

The number 1120, *in base 3*, means:

(1 * 3^3) + (1 * 3^2) + (2 * 3^1) + (0 * 3^0)

I think you got the idea!

*Yes. Those three numbers above are exactly the same. Congratulations!*

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
module Test.Main where
import Prelude
import Control.Monad.Eff (Eff)
import Control.Monad.Eff.AVar (AVAR)
import Control.Monad.Eff.Console (CONSOLE)
import Data.Maybe (Maybe(..))
import Test.Unit.Assert as Assert
import Test.Unit (TestSuite, suite, test)
import Test.Unit.Console (TESTOUTPUT)
import Test.Unit.Main (runTest)
import AllYourBase (rebase)
main :: forall eff
. Eff ( avar :: AVAR
, console :: CONSOLE
, testOutput :: TESTOUTPUT
| eff
)
Unit
main = runTest suites
suites :: forall e. TestSuite e
suites = do
suite "AllYourBase.rebase" do
test "single bit one to decimal" $
Assert.equal (Just [1])
(rebase 2 10 [1])
test "binary to single decimal" $
Assert.equal (Just [5])
(rebase 2 10 [1,0,1])
test "single decimal to binary" $
Assert.equal (Just [1,0,1])
(rebase 10 2 [5])
test "binary to multiple decimal" $
Assert.equal (Just [4,2])
(rebase 2 10 [1,0,1,0,1,0])
test "decimal to binary" $
Assert.equal (Just [1,0,1,0,1,0])
(rebase 10 2 [4,2])
test "trinary to hexadecimal" $
Assert.equal (Just [2,10])
(rebase 3 16 [1,1,2,0])
test "hexadecimal to trinary" $
Assert.equal (Just [1,1,2,0])
(rebase 16 3 [2,10])
test "15-bit integer" $
Assert.equal (Just [6,10,45])
(rebase 97 73 [3,46,60])
test "empty list" $
Assert.equal Nothing
(rebase 2 10 [])
test "single zero" $
Assert.equal Nothing
(rebase 10 2 [0])
test "multiple zeros" $
Assert.equal Nothing
(rebase 10 2 [0,0,0])
test "leading zeros" $
Assert.equal Nothing
(rebase 7 10 [0,6,0])
test "negative digit" $
Assert.equal Nothing
(rebase 2 10 [1,-1,1,0,1,0])
test "invalid positive digit" $
Assert.equal Nothing
(rebase 2 10 [1,2,1,0,1,0])
test "first base is one" $
Assert.equal Nothing
(rebase 1 10 [])
test "second base is one" $
Assert.equal Nothing
(rebase 2 1 [1,0,1,0,1,0])
test "first base is zero" $
Assert.equal Nothing
(rebase 0 10 [])
test "second base is zero" $
Assert.equal Nothing
(rebase 10 0 [7])
test "first base is negative" $
Assert.equal Nothing
(rebase (-2) 10 [1])
test "second base is negative" $
Assert.equal Nothing
(rebase 2 (-7) [1])
test "both bases are negative" $
Assert.equal Nothing
(rebase (-2) (-7) [1])
```

```
module AllYourBase where
import Prelude
import Data.Array (find, foldl, head)
import Data.Maybe (Maybe(..), isJust)
type Base = Int
toDigits :: Base -> Int -> Array Int
toDigits b n = toDigits' [] n where
toDigits' :: Array Int -> Int -> Array Int
toDigits' acc m
| m > 0 = toDigits' ([m `mod` b] <> acc) (m / b)
| otherwise = acc
fromDigits :: Base -> Array Int -> Int
fromDigits b = foldl (\n x -> b * n + x) 0
invalid :: Array Int -> Boolean
invalid digits = case head digits of
Nothing -> true
Just 0 -> true
_ -> false
rebase :: Int -> Int -> Array Int -> Maybe (Array Int)
rebase from to digits
| from <= 1 = Nothing
| to <= 1 = Nothing
| invalid digits = Nothing
| isJust $ find (\x -> x < 0 || x >= from) digits = Nothing
| otherwise = Just $ toDigits to $ fromDigits from digits
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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