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The Fourier domain acceleration search (FDAS) is an effective technique for detecting faint binary pulsars in large radio astronomy data sets. This paper quantifies the sensitivity impact of reducing numerical precision in the graphics processing unit (GPU)-accelerated FDAS pipeline of the AstroAccelerate (AA) software package. The prior implementation used IEEE-754 single-precision in the entire binary pulsar detection pipeline, spending a large fraction of the runtime computing GPU-accelerated fast Fourier transforms. AA has been modified to use bfloat16 (and IEEE-754 double-precision to provide a "gold standard" comparison) within the Fourier domain convolution section of the FDAS routine. Approximately 20,000 synthetic pulsar filterbank files representing binary pulsars were generated using SIGPROC with a range of physical parameters. They have been processed using bfloat16, single-precision, and double-precision convolutions. All bfloat16 peaks are within 3% of the predicted signal-to-noise ratio of their corresponding single-precision peaks. Of 14,971 "bright" single-precision fundamental peaks above a power of 44.982 (our experimentally measured highest noise value), 14,602 (97.53%) have a peak in the same acceleration and frequency bin in the bfloat16 output plane, while in the remaining 369 the nearest peak is located in the adjacent acceleration bin. There is no bin drift measured between the single- and double-precision results. The bfloat16 version of FDAS achieves a speedup of approximately 1.6x compared to single-precision. A comparison between AA and the PRESTO software package is presented using observations collected with the GMRT of PSR J1544+4937, a 2.16 ms black widow pulsar in a 2.8 hr compact orbit.