binadd.rb

#!/usr/bin/ruby

class Integer

  def to_b
    Bin.new 0 == self ? [] : [self % 2] + (self / 2).to_b
  end

end


class Bin < Array

  def + a
    Bin.new (0..[self.length, a.length].max - 1).map { |n| (self[n] || 0) + (a[n] || 0) }
  end

  def to_i
    self.reverse.reduce { |a, n| (a << 1) + n } || 0
  end

end

puts (3.to_b + 15.to_b).to_i

binadd_spec.rb

require './binadd'

r = Random.new 1234

describe Integer, '#to_b' do
  it 'converts a number into a binary representation' do

    0.to_b.to_i.should eq(0)
    
    10000.times do
      n = r.rand(0..1073741823)
      n.to_b.to_i.should eq(n)
    end

  end
end

describe Bin, '#+@' do
  it 'should add two binary values' do

    10000.times do
      a = r.rand(0..1073741823)
      b = r.rand(0..1073741823)
      (a.to_b + b.to_b).to_i.should eq(a + b)
    end

  end
end