A memory controller for receiving a differential data strobe signal and an application processor having the memory controller are disclosed. The memory controller includes a strobe signal receiver configured to receive first and second strobe signals from a memory device as differential data strobe signal and output a first detection signal based on a level of each of the first and second strobe signals, a comparator configured to receive the second strobe signal and a reference voltage and compare a level of the second strobe signal with a level of the reference voltage to output a second detection signal, and a gate signal generator configured to generate a gate signal masking a portion of a period corresponding to the differential data strobe signal using the first detection signal and the second detection signal.