Dynamically increment number in query / Oracle database

You must have a way to totally order the input rows. ("Total" ordering means "no ties".)

Other than that, you can do this easily with match_recognize, as shown below. In the output I included the ordering column (I assumed a numeric column, but it can be a date, etc. - whatever you can use to totally order the inputs) and I included both the original and the new values; if you only need the new values, you can control that in the select clause.

The input data in the with clause is there just for easy testing; you will need to remove it, and to use your actual table and column names in the query.

with
  sample_inputs (ord, val) as (
    select  1, 0 from dual union all
    select  2, 0 from dual union all
    select  3, 1 from dual union all
    select  4, 1 from dual union all
    select  5, 1 from dual union all
    select  6, 0 from dual union all
    select  7, 0 from dual union all
    select  8, 0 from dual union all
    select  9, 0 from dual union all
    select 10, 1 from dual union all
    select 11, 1 from dual union all
    select 12, 1 from dual union all
    select 13, 1 from dual union all
    select 14, 1 from dual union all
    select 15, 1 from dual union all
    select 16, 0 from dual union all
    select 17, 0 from dual
  )
select ord, val, new_val
from   sample_inputs
match_recognize (
  order by ord
  measures count(a.val) as new_val
  all rows per match
  pattern  ( a+ | b+ )
  define   a as val = 1, b as val = 0
);

OUTPUT:

       ORD        VAL    NEW_VAL
---------- ---------- ----------
         1          0          0
         2          0          0
         3          1          1
         4          1          2
         5          1          3
         6          0          0
         7          0          0
         8          0          0
         9          0          0
        10          1          1
        11          1          2
        12          1          3
        13          1          4
        14          1          5
        15          1          6
        16          0          0
        17          0          0

This assumes that your intent is to "count" the values (rather than, for example, "sum" them). If all the input values are 0 and 1, then it makes no difference. If you may also have other non-zero values (other than 1), and you must "sum" them instead of counting them, that's a simple modification to the query - use sum(val) in the measures clause. In both cases, with the all rows per match clause, the query will compute cumulative values (cumulative count, resp. cumulative sum).