This paper presents a 56-Gb/s PAM4 transceiver using an ADC-based RX with a false-lock-aware locking scheme for Mueller-Müller (MM) CDR. After the false-lock-aware locking scheme, a clock phase is adjusted to achieve maximum eye height by using a post-1-tap parameter for an FFE in the CDR loop. A PLL uses an area-efficient “glasses-shaped” inductor. The RX comprises an AFE, a 28-GS/s 7-bit time-interleaved SAR ADC, and a DSP with a 31-tap FFE and a 1-tap DFE. A TX is based on a 7-bit DAC with a 4-tap FFE. The transceiver is fabricated in 16-nm CMOS FinFET technology, and achieves a BER of less than 1e-7 with a 30-dB loss channel. The measurement results show that the MM CDR escapes from false-lock points, and converges to near the optimum point for large eye height.