nemerle, 489 bytes

Result [link]

AC

Code [DL]

using System;
public class Test
{
	public static Main() : void
	{
		def s = System.Console.ReadLine();
		def arr : array[int] = array(150);
		for(mutable i = 55; i>=0;i--) {
			arr[i] = 0;
		}
		for(mutable n = 0; n < 100; ++n) {
			for(mutable i = 50; i>=0;i--) {
				arr[i] *= 2;
				arr[i+1] += arr[i] / 10;
				arr[i] %= 10;
  			}
   			if(s[n]=='1'){
  			  arr[0] += 1;
  			} else {
  			}
		}
		for(mutable i = 50; i>=0;i--) {
    		System.Console.Write("{0}",arr[i]);
    	}
	}
}

stdin

0011100111011100110111000001100010000011010011111010110001011010001101011001111011000100001001011101

stdout

000000000000000000000286522377807071156356791419485

stderr

strace