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We have proposed a multi-bit sigma-delta analog-to-digital converter (ADC) in which a modulator is composed of a single quantizer and multiple samplers based on the single-flux-quantum (SFQ) circuits. The quantizer converts analog signals to pulse-density-modulated signals, and the samplers sample the modulated SFQ pulses in every sampling clock. Use of multiple samplers based on delayed-flip-flops (DFFs) increases sampling frequencies virtually, resulting in a multi-bit sigma-delta modulator. We also designed a decimation filter by using the well-established Verilog tools for the SFQ circuits and the Matlab simulator. We prepared an ADC including 4 samplers and a second-order decimation filter with the decimation rate of 1:256 based on the Nb junction technology. We confirmed correct operation of this ADC at 56 GHz clock signals generated by an internal ring oscillator. We experimentally obtained the signal-to-noise ratio of 25 dB and spurious-free dynamic range of 37 dB at the bandwidth of 10 MHz from the upper 7 bits of the outputs of the decimation filter.