To uphold the security of individuals, analyzing the amount of information in binary biometric representation is highly essential. While Shannon entropy is a measure to quantify the expected value of information in the binary representation, it does not account the extent to which every binary representation could distinctively identify a person in a population. Hence, it does not appropriately quantify the hardness of obtaining a close approximation of the user's biometric template if one maliciously leverages the population distribution. To resolve this, relative entropy has been used to measure information of user distribution with reference to the population distribution. However, existing relative-entropy estimation techniques that are based on statistical methods in the Euclidean space cannot be directly extended to the Hamming space. Therefore, we put forward a new entropy measure known as distance entropy and its estimation technique to quantify the information in binary biometric representation more effectively with respect to the discrimination power of the binary representation.