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We study a single-shot single-flux-quantum (SFQ) readout circuit based on current-to-time conversion for superconducting flux qubits. Circulating currents representing states of a qubit were converted to propagation delay time of SFQ pulses, and then detected by a time discriminator. The key parameter which determines the availability of single-shot readout is current resolution. We evaluated the current resolution by measuring the gray zone which was defined as the transition width in the output probability of the current-to-time converter with 1000 trials for each value of an input current. For reducing unwanted effects on the qubit, shunt resistors are required to be removed for Josephson junctions in the readout circuit. We designed two readout circuits for comparison, the circuit composed of shunted junctions and that of unshunted junctions. Gray zones were measured to be 4.8 muA for unshunted junctions and 2.2 muA for the shunted ones at 4.2 K. These gray zones may originate from Johnson noise. Operation at a reduced temperature and employment of a likelihood decision circuit will lead to reduced gray zone, i.e., improved current resolution sufficient for single-shot readout.