I/O blocks include input, output, and output enable circuits for interfacing with memory devices. The input circuit includes registers for capturing a double data rate signal, converting it into single data rate signals, and resynchronizing the single data rate signals. Multiple devices may be accessible with each device potentially having a different clock signal for resynchronizing. Another clock signal may be used to align/synchronize resulting signals from multiple devices. The resynchronized single rate signals can be converted into half-rate data signals, and the four half-rate data signals can be provided to resources in the programmable device core. The input circuit also may provide a half-rate clock signal synchronized with the half-rate data signals to the programmable device core. The half rate clock signal can be derived from the full-rate clock signal using a data strobe signal, a full-rate clock signal, or a half-rate clock signal as an input.