Binary Addition with logic gates

gistfile1.rb

class Array
  def second
    self[1]
  end
end
class Integer
  def one?
    raise "Not Binary" unless self == 1 || self == 0
    self == 1
  end
end

def _or(first, second)
  _nand(_nand(first,first), _nand(second,second))
end

def _and(first, second)
  _nand(_nand(first, second), _nand(first, second))
end

def _nand(first, second)
  first.one? && second.one? ? 0 : 1
end

def _nor(first, second)
  _not(_or(first, second))
end

def _not(bit)
  _nand(bit, bit)
end

def _xor(first, second)
  _and(_or(first, second), _nand(first, second))
end

def _xnor(first, second)
  _not(xor(first, second))
end

def sum(first, second)
  _xor(first, second)
end

def carry(first, second)
  _and(first, second)
end

def half_adder(first, second)
  [sum(first, second), carry(first, second)]
end

def full_adder(first, second, carry)
  first_calc = half_adder(first, second)
  second_calc = half_adder(carry, first_calc.first)
  [second_calc.first, _or(second_calc.second, first_calc.second)]
end

def split_reverse(string)
  string.reverse.split("").map(&:to_i)
end

def print_question(first, second, operation)
  puts "  #{first}    (#{to_decimal(first)})"
  puts "#{operation} #{second}    (#{to_decimal(second)})"
  puts "  #{"-"  * first.length}"
end

def do_addition(first, second)
  first, second = split_reverse(first), split_reverse(second)
  answer = first.zip(second).inject(["", 0]) do |partial_answer, next_pair|
    addition = full_adder(next_pair.first, next_pair.second, partial_answer.second)
    [addition.first.to_s + partial_answer.first, addition.second]
  end
  answer.second.to_s + answer.first
end

def add(first, second)
  print_question(first, second, "+")
  answer = do_addition(first, second)
  puts " #{answer}    (#{to_decimal(answer)})"
end

def to_decimal(binary)
  split_reverse(binary).each_with_index.inject(0) do |sum, next_digit|
    sum + (next_digit.first * (2 ** next_digit.second))
  end
end

add("00011010", "00001100")

#   00011010    (26)
# + 00001100    (12)
#   --------
#  000100110    (38)