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Add exercise all-your-base.
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‎all-your-base.json

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{
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"#": [ "It's up to each track do decide:"
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, ""
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, "1. What's the canonical representation of zero?"
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, " - []?"
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, " - [0]?"
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, ""
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, "2. What representations of zero are allowed?"
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, " - []?"
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, " - [0]?"
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, " - [0,0]?"
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, ""
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, "3. Are leading zeroes allowed?"
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, ""
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, "4. How should invalid input be handled?"
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, ""
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, "All the undefined cases are marked as null."
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, ""
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, "All your numeric-base are belong to [2..]. :)"
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],
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"cases": [
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{ "description" : "single bit one to decimal"
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, "input_base" : 2
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, "input_digits" : [1]
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, "output_base" : 10
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, "output_digits": [1]
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},
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{ "description" : "binary to single decimal"
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, "input_base" : 2
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, "input_digits" : [1, 0, 1]
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, "output_base" : 10
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, "output_digits": [5]
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},
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{ "description" : "single decimal to binary"
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, "input_base" : 10
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, "input_digits" : [5]
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, "output_base" : 2
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, "output_digits": [1, 0, 1]
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},
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{ "description" : "binary to multiple decimal"
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, "input_base" : 2
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, "input_digits" : [1, 0, 1, 0, 1, 0]
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, "output_base" : 10
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, "output_digits": [4, 2]
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},
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{ "description" : "decimal to binary"
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, "input_base" : 10
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, "input_digits" : [4, 2]
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, "output_base" : 2
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, "output_digits": [1, 0, 1, 0, 1, 0]
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},
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{ "description" : "trinary to hexadecimal"
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, "input_base" : 3
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, "input_digits" : [1, 1, 2, 0]
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, "output_base" : 16
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, "output_digits": [2, 10]
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},
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{ "description" : "hexadecimal to trinary"
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, "input_base" : 16
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, "input_digits" : [2, 10]
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, "output_base" : 3
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, "output_digits": [1, 1, 2, 0]
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},
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{ "description" : "15-bit integer"
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, "input_base" : 97
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, "input_digits" : [3,46,60]
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, "output_base" : 73
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, "output_digits": [6,10,45]
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},
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{ "description" : "empty list"
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, "input_base" : 2
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, "input_digits" : []
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "single zero"
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, "input_base" : 10
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, "input_digits" : [0]
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, "output_base" : 2
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, "output_digits": null
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},
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{ "description" : "multiple zeros"
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, "input_base" : 10
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, "input_digits" : [0, 0, 0]
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, "output_base" : 2
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, "output_digits": null
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},
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{ "description" : "leading zeros"
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, "input_base" : 7
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, "input_digits" : [0, 6, 0]
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "negative digit"
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, "input_base" : 2
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, "input_digits" : [1, -1, 1, 0, 1, 0]
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "invalid positive digit"
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, "input_base" : 2
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, "input_digits" : [1, 2, 1, 0, 1, 0]
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "first base is one"
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, "input_base" : 1
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, "input_digits" : []
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "second base is one"
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, "input_base" : 2
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, "input_digits" : [1, 0, 1, 0, 1, 0]
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, "output_base" : 1
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, "output_digits": null
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},
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{ "description" : "first base is zero"
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, "input_base" : 0
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, "input_digits" : []
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "second base is zero"
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, "input_base" : 10
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, "input_digits" : [7]
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, "output_base" : 0
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, "output_digits": null
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},
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{ "description" : "first base is negative"
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, "input_base" : -2
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, "input_digits" : [1]
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, "output_base" : 10
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, "output_digits": null
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},
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{ "description" : "second base is negative"
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, "input_base" : 2
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, "input_digits" : [1]
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, "output_base" : -7
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, "output_digits": null
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},
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{ "description" : "both bases are negative"
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, "input_base" : -2
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, "input_digits" : [1]
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, "output_base" : -7
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, "output_digits": null
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} ]
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}

‎all-your-base.md

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Implement general base conversion. Given a number in base **a**,
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represented as a sequence of digits, convert it to base **b**.
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## Note
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- Try to implement the conversion yourself.
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Do not use something else to perform the conversion for you.
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## About [Positional Notation](https://en.wikipedia.org/wiki/Positional_notation)
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In positional notation, a number in base **b** can be understood as a linear
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combination of powers of **b**.
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The number 42, *in base 10*, means:
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(4 * 10^1) + (2 * 10^0)
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The number 101010, *in base 2*, means:
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(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
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The number 112, *in base 3*, means:
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(1 * 3^2) + (1 * 3^1) + (2 * 3^0)
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I think you got the idea!
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*Yes. Those three numbers above are exactly the same. Congratulations!*

‎all-your-base.yml

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---
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blurb: "Write a program that will convert a number, represented as a sequence of digits in one base, to any other base."

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