Explanation : The largest decimal number with 25 digits is 9,999,999,999,999,999,999,999,999. The smallest decimal number in the form 2n-1 which is greater than or equal to that is 19,342,813,113,834,066,795,298,815. That corresponds to 284-1. So, the minimum number of binary bits required to represent the decimal number 25 nines in a row is 84.
This is 84 ones in a row. If you want to support negative as well as positive numbers, you will need 85.