One of well-known results is that the greatest eigenvalue of a nonnegative matrix lies between the smallest and the largest row sum.

Of course, you can use a similar approach, by computing the sum of the elements in each row and remembering which row is the smallest you've seen so far.

The "cumulative row to binary number" mapping is the same as the previous mapping, but you keep a cumulative sum — a running total — of the row values.