Lookup table circuits programmable to implement flip-flops

A lookup table (LUT) is programmable to function as a flip-flop. The LUT includes a plurality of memory cells, a plurality of transmission gates, and first and second logic gates. The transmission gates are coupled between the memory cells and an output terminal of the LUT to form a multiplexer circuit selecting one of a plurality of values stored in the memory cells and providing the selected value to the output terminal. First and second logic gates are included in two of the paths through the multiplexer, also providing first and second feedback paths within the LUT. These feedback paths enable the programmable implementation of first and second latches that form the flip-flop. Another subset of the memory cells can be optionally used to implement a function that drives the data input of the flip-flop.