# All Your Base

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**.

## Note

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

## About [Positional Notation](https://en.wikipedia.org/wiki/Positional_notation)

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!*

## Implementation

Assumptions:
1. Zero is always represented in outputs as [0] instead of [].
2. In no other instances are leading zeroes present in any outputs.
3. Leading zeroes are accepted in inputs.
4. An empty sequence of input digits is considered zero, rather than an error.

Handle problem cases by returning an error whose Error() method
returns one of following messages:
* input base must be >= 2
* output base must be >= 2
* all digits must satisfy 0 <= d < input base


## Running the tests

To run the tests run the command `go test` from within the exercise directory.

If the test suite contains benchmarks, you can run these with the `-bench`
flag:

    go test -bench .

Keep in mind that each reviewer will run benchmarks on a different machine, with
different specs, so the results from these benchmark tests may vary.

## Further information

For more detailed information about the Go track, including how to get help if
you're having trouble, please visit the exercism.io [Go language page](http://exercism.io/languages/go/about).

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