awk, 401 bytes

Result [link]

WA

Code [DL]

END{
    str = $0
    for(i = 0; i < 100; i++){
       bin[i] = int(substr(str, i - 1, 1))
    }
    
    for(i = 0; i < 34; i++){
    	rem = 0
        for(j = 0; j < 100; j++){
        	rem *= 2
			rem += bin[j]
			bin[j] = int(rem / 10)
			rem %= 10
		}
        
        dec[i] = rem
    }
    
    deci = ""
    
    for(i = 0; i < 34; i++){
    	deci = deci dec[33 - i]
    }
    
    print deci
}

stdin

0011101101011111011011110110010100110101100101001101001100100111111000000000011000110110000110111111

stdout

0000000000000000000000000000000000

stderr

strace