This dissertation presents the design and development of a mixed-signal low noise second-order integrated circuit (IC) for the open-loop and closed-loop operation of integrated capacitive micro- and nano-gravity accelerometers. The micromechanical accelerometers are fabricated in thick (less than 100 m) silicon-on-insulator (SOI) substrates. The IC provides the 1-bit digital output stream and has the versatility of interfacing sensors with different sensitivities while maintaining minimum power consumption (less than 5 mW) and maximum dynamic range (90 dB). A fully-differential sampled-data scheme is deployed with the ability of low-frequency noise reduction through the use of correlated double sampling (CDS) scheme. In this work, the measured resolution of the closed-loop CMOS-SOI accelerometer system, in the presence of high background accelerations, is in the micro-g (g: gravity) range. In this design, a second-order SC modulator is cascaded with the accelerometer and the front-end amplifier. The accelerometer operates in air and is designed for non-peaking response with a BW-3dB of 500 Hz. A 22 dB improvement in noise and hence dynamic range is achieved with a sampling clock of 40 kHz corresponding to a low oversampling ratio (OSR) of 40. The interface IC consumed a current of 1.5 mA from a supply of 3 V.