A new silicon-strip readout chip named SliT has been developed for the measurement of the muon anomalous magnetic moment and electric dipole moment at J-PARC. The SliT is designed in the Silterra 180 nm CMOS technology with mixed-signal integrated circuits. An analog circuit incorporates a conventional charge-sensitive amplifier, shaping amplifiers, and two distinct discriminators for each of 128 identical channels. A digital part includes storage memories, an event building block, a serializer, and LVDS drivers. A distinct feature of the SliT is utilization of the zero-cross architecture, which consists of a CR-RC filter followed by a CR circuit as a voltage differentiator. This architecture enables to generate hit signals with subnanosecond amplitude-independent time walk, which is the primary requirement for the experiment. The test results show the time walk of $0.38 pm 0.16$ ns between 0.5 and 3 MIP signals. The equivalent noise charge is $1547 pm 75 $ $e^{-}$ (rms) at $C_{rm det} = 33$ pF as a strip-sensor capacitance. Other functionalities such as a strip-sensor readout chip have also been proven in the tests. The SliT128C satisfies all requirements of the J-PARC muon $g-2$/EDM experiment.
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