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# Binary
Convert a binary number, represented as a string (e.g. '101010'), to its decimal equivalent using first principles.
Implement binary to decimal conversion. Given a binary input
string, your program should produce a decimal output. The
program should handle invalid inputs.
## Note
- Implement the conversion yourself.
Do not use something else to perform the conversion for you.
## About Binary (Base-2)
Decimal is a base-10 system.
A number 23 in base 10 notation can be understood
as a linear combination of powers of 10:
- The rightmost digit gets multiplied by 10^0 = 1
- The next number gets multiplied by 10^1 = 10
- ...
- The *n*th number gets multiplied by 10^*(n-1)*.
- All these values are summed.
So: `23 => 2*10^1 + 3*10^0 => 2*10 + 3*1 = 23 base 10`
Binary is similar, but uses powers of 2 rather than powers of 10.
So: `101 => 1*2^2 + 0*2^1 + 1*2^0 => 1*4 + 0*2 + 1*1 => 4 + 1 => 5 base 10`.
* * * *
For installation and learning resources, refer to the
[exercism help page](http://exercism.io/languages/ruby).
For running the tests provided, you will need the Minitest gem. Open a
terminal window and run the following command to install minitest:
gem install minitest
If you would like color output, you can `require 'minitest/pride'` in
the test file, or note the alternative instruction, below, for running
the test file.
Run the tests from the exercise directory using the following command:
ruby binary_test.rb
To include color from the command line:
ruby -r minitest/pride binary_test.rb
## Source
All of Computer Science [http://www.wolframalpha.com/input/?i=binary&a=*C.binary-_*MathWorld-](http://www.wolframalpha.com/input/?i=binary&a=*C.binary-_*MathWorld-)
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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