cobol85, 637 bytes

Result [link]

WA

Code [DL]

IDENTIFICATION DIVISION.
PROGRAM-ID. IDEONE.
 
ENVIRONMENT DIVISION.
 
DATA DIVISION.
WORKING-STORAGE SECTION.
01 b PIC X(100) .
01 i PIC 9(3) .
01 du PIC 9(16) VALUE 0.
01 dl PIC 9(16) VALUE 0.
01 d PIC X(31) .
01 m PIC 9(16) VALUE 1000000000000000.
01 c PIC 9 .
01 q PIC 9 .
01 r PIC 9(16) .
 
PROCEDURE DIVISION.
  ACCEPT b
  PERFORM VARYING i FROM 1 BY 1 UNTIL i > 100
    COMPUTE du = du * 2
    COMPUTE dl = dl * 2
    MOVE b(i:1) TO c
    COMPUTE dl = dl + c
    DIVIDE dl BY m GIVING q REMAINDER r
    MOVE r TO dl
    COMPUTE du = du + q
  END-PERFORM.
  STRING
    du dl(2:15)
    INTO d
  END-STRING.
  DISPLAY d.
  STOP RUN.

stdin

1101101001111100011110010011001011010101000001001010111010010010101111110001100011110011010111111111

stdout

1081891380587466484599908939262

stderr

strace