A system for computing a block floating point scaling factor by detecting a dynamic range of an input signal in a central processing unit without additional overhead cycles is provided. The system includes a dynamic range monitoring unit that detects the dynamic range of the input signal by snooping outgoing write data and incoming memory read data of the input signal. The dynamic range monitoring unit includes a running maximum count unit that stores a least value of a count of leading zeros and leading ones, and a running minimum count that stores a least value of the count of trailing zeros. The dynamic range is detected based on the least value of the count of leading zeros and leading ones and the count of trailing zeros. The system further includes a scaling factor computation module that computes the block floating point (BFP) scaling factor based on the dynamic range.