The objective of this thesis is to demonstrate the application of baud-rate clock and data recovery in a 56-Gb/s NRZ receiver with TSMC standard digital 40nm CMOS technology. This architecture can share data decision and phase detection comparators, greatly reduce the number of comparators, power consumption, the internal circuit , including variable gain amplifier, continuous time equalizer, one-tap decision feedback equalizer, and all digital clock data recovery circuit based on phase interpolator.