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We propose a single-flux-quantum (SFQ) based readout circuit for a transition edge sensor (TES) array for X-ray radiation detection. Utilization of SFQ circuits for this purpose enables large-scale integration of TESs due to very high speed processing ability of the received signals and using an already established integrated circuit design environment. We utilize the cooling time dependence of the TES on the incident X-ray energy. Time to digital conversion is made by using an SFQ based quasi-one-junction SQUID (QOS), which works as a 1-bit comparator with an adjustable current threshold level, and an SFQ based high speed counter. The readout system is composed of two separate chips that are connected to each other with flexible superconducting wiring. The QOS-multiplexer chip is directly connected to the TES array and it performs the digital conversion of the TES output. The demultiplexer-counter chip, which will be placed at elevated temperatures, receives the multiplexed SFQ pulses and determines the duration of the TES output which is above the predetermined threshold level. Final goal of this work is to readout more than 10 k TES pixels and in this paper, feasibility of the system and current status of the development process is demonstrated.