The design and implementation of an analog floating-point sampling integrated circuit for the BaBar detector at the SLAG B-Factory is described. The CARE (Custom Auto-Range Encoding) circuit is part of an 18-bit dynamic range sampling system with a 4-MHz waveform digitization rate for the CsI calorimeter. The architecture and methodology of the system are described. The CARE integrated circuit receives dual-range (gain of 1 and 32) 13-bit signals from the 18-bit range preamplifiers mounted directly on the CsI crystals and converts the input at a rate of 4 MHz to an auto-range floating-point format with a 10-bit analog mantissa and 2 digital range bits (for 4 ranges). Additional functions integrated on the chip are averaging and selection circuitry for signals originating from two independent diodes per crystal and range-selection overwrite circuitry. The circuit will be mounted within the detector structure and thus low power dissipation is essential. The circuit has been fabricated in a 1.2-mu m BiCMOS process with polysilicon-to-polysilicon capacitors and polysilicon resistors. Measurement results are presented. One complete CARE channel dissipates 25 mW.