Binary conversion app
Welcome to SO and glad you are learning Ruby.
You know there are easy ways in Ruby to do convertions between numbers ?
If not take a look at this blog http://rubyquicktips.com/post/18935873770/convert-between-number-bases-easily

Answering your question: you have a lot of boiler code which you could cut by taking the exponent of each digit like here under. While I still could do this shorter by injecting an object instead of declaring the dec = 0 I won't do so for readability.

I use the method each_char on the string to split into a character array and daisychain this result to another method with_index that adds... yes an index.
Then I use the formula below to add the exponent of that char multiplied by 2 (the base) converted to an integer taking into account the position in the string.
This is not the best algorithm by far to do this, just an example how to use these methods to shorten your code and make it more 'Rubylike'.
If you search for good exercises which you can test and compare your results with others solutions taka a look at https://www.codewars.com

Happy code learning !

bin_input = "1111"
puts bin_input.to_i(2)  #=&gt; 15 this is the normal Ruby way

# This is our educational way
dec = 0
print dec
bin_input.to_s.each_char.with_index do |char, index|
  dec += (char.to_i*2)**(bin_input.length-(index+1))
  puts "+(#{char.to_i*2})**(#{bin_input.length-(index+1)})"
end
puts dec # 15


Which gives

15
0+(2)**(3)
+(2)**(2)
+(2)**(1)
+(2)**(0)
15