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We have been developing a large-scale reconfigurable data-path (LSRDP) based on single-flux-quantum (SFQ) circuits to establish a fundamental technology for future high-performance computing systems. The SFQ floating-point adder (FPA) is one of the principal and most complicated circuit blocks in an LSRDP. In this study, we designed and implemented component circuits of an SFQ bit-serial half-precision FPA using the cell library for a 10-kA/cm2 Nb process and performed on-chip high-speed tests. We demonstrated correct operation of the four-bit shifter for the significand at the clock frequencies of up to 76 GHz. The dependence of the measured DC bias margin on the operating frequency agrees reasonably well with the margin calculated using a digital simulation. The operation of the normalizer for the significand has been also confirmed at low speeds.