For orthogonal frequency division multiplexing (OFDM) systems, the carrier frequency offset (CFO) estimation is required for the frequency synchronization before the data reception. When 1-bit ADCs are employed in OFDM systems, the available information is limited to the sign of the received signal, and the acquisition of the CFO is not easy problem. To overcome this limitation, we utilize the extended preamble and construct the bank of the CFO estimators based on auto-correlation (AC) taking the samples from the preamble with flexible intervals, which produces the candidates for CFO estimate. We propose the CFO estimation algorithms using the normalized squared errors (NSEs) as the concept to check the quality of the candidates of CFO estimate. The simulation results show that the proposed algorithm works well in the multipath fading channel, and is superior to the conventional CFO estimation method based on AC with fixed interval.