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# Nia11's solution

## to All Your Base in the Lua Track

Published at Dec 21 2018 · 0 comments
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.

## Note

• 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!

## Running the tests

To run the tests, run the command `busted` from within the exercise directory.

## Further information

For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.

## Submitting Incomplete Solutions

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

### all-your-base_spec.lua

``````local all_your_base = require 'all-your-base'

describe('all-your-base', function()
it('should convert a single binary digit to a single decimal digit', function()
assert.are.same({ 1 }, all_your_base.convert({ 1 }, 2).to(10))
end)

it('should convert multiple binary digits to a single decimal digit', function()
assert.are.same({ 5 }, all_your_base.convert({ 1, 0, 1 }, 2).to(10))
end)

it('should convert a single decimal digit to binary', function()
assert.are.same({ 1, 0, 1 }, all_your_base.convert({ 5 }, 10).to(2))
end)

it('should convert binary to decimal', function()
assert.are.same({ 1, 0, 1, 0, 1, 0 }, all_your_base.convert({ 4, 2 }, 10).to(2))
end)

it('should convert decimal to binary', function()
assert.are.same({ 4, 2 }, all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(10))
end)

it('should convert trinary to hexadecimal', function()
assert.are.same({ 2, 10 }, all_your_base.convert({ 1, 1, 2, 0 }, 3).to(16))
end)

it('should convert hexadecimal to trinary', function()
assert.are.same({ 1, 1, 2, 0 }, all_your_base.convert({ 2, 10 }, 16).to(3))
end)

it('should convert between large bases', function()
assert.are.same({ 6, 10, 45 }, all_your_base.convert({ 3, 46, 60 }, 97).to(73))
end)

it('should convert no digits to 0', function()
assert.are.same({ 0 }, all_your_base.convert({ }, 2).to(10))
end)

it('should convert no digits to 0', function()
assert.are.same({ 0 }, all_your_base.convert({ }, 10).to(2))
end)

it('should convert multiple 0 digits to 0', function()
assert.are.same({ 0 }, all_your_base.convert({ 0, 0, 0 }, 10).to(2))
end)

assert.are.same({ 4, 2 }, all_your_base.convert({ 0, 6, 0 }, 7).to(10))
end)

it('should not allow negative digits', function()
assert.has_error(function()
all_your_base.convert({ 1, -1, 1, 0, 1, 0 }, 2).to(10)
end, 'negative digits are not allowed')
end)

it('should not allow digits that are out of range', function()
assert.has_error(function()
all_your_base.convert({ 1, 2, 1, 0, 1, 0 }, 2).to(10)
end, 'digit out of range')
end)

it('should not allow an input base less than 2', function()
assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, -1).to(10)
end, 'invalid input base')

assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 0).to(10)
end, 'invalid input base')

assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 1).to(10)
end, 'invalid input base')
end)

it('should not allow an output base less than 2', function()
assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(-1)
end, 'invalid output base')

assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(0)
end, 'invalid output base')

assert.has_error(function()
all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(1)
end, 'invalid output base')
end)
end)``````
``````base={}

function base.convert(digits,base)
assert(base>=2,'invalid input base')
local base10 = 0
for i=1,#digits do
assert(digits[i]<base,'digit out of range')
assert(digits[i]>=0,'negative digits are not allowed')
base10 = base10 + digits[i] * base^(#digits-i)
end
return{
to = function(new_base)
assert(new_base>=2,'invalid output base')
local new_digits = {}
if base10==0 then new_digits={0} end
while base10>0 do
table.insert(new_digits,1,base10%new_base)
base10 = math.floor(base10/new_base)
end
return new_digits
end
}

end

return base``````

### What can you learn from this solution?

A huge amount can be learned from reading other peopleâ€™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?