def binary_xor(x, y)
  raise 'Input must only contain positive integers' if x < 0 or y < 0

  binary_x = x.to_s(2)
  binary_y = y.to_s(2)

  if binary_x.length > binary_y.length
    prefix = "0" * (binary_x.length - binary_y.length)
    binary_y = prefix + binary_y
  elsif binary_y.length > binary_x.length
    prefix = "0" * (binary_y.length - binary_x.length)
    binary_x = prefix + binary_x
  end
  result = "0b"
  binary_x.each_char.with_index do |x_char, i|
    y_char = binary_y[i]

    if (x_char == "1" && y_char != "1") || (x_char != "1" && y_char == "1")
      result += "1"
    else
      result += "0"
    end
  end

  result
end

begin
  binary_xor(-1, 0)
rescue => e
  puts e.message
end

puts binary_xor(1, 1)
# 0b0
puts binary_xor(0, 1)
# 0b1
puts binary_xor(1024, 1024)
# 0b00000000000
puts binary_xor(0, 1023)
# 0b1111111111
puts binary_xor(16, 58)
# 0b101010