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A biometric discretization scheme converts biometric features into a binary string via segmenting every one-dimensional feature space into multiple labelled intervals, assigning each interval-captured feature element with a short binary string and concatenating the binary output of all feature elements into a bit string. This paper proposes a bit allocation algorithm for biometric discretization to allocate bits dynamically to every feature element based on a Binary Reflected Gray code. Unlike existing bit allocation schemes, our scheme bases upon a combination of bit statistics (reliability measure) and signal to noise ratio (discriminability measure) in performing feature selection and bit allocation procedures. Several empirical comparative studies are conducted extensively on two popular face datasets to justify the efficiency and feasibility of our proposed approach.