A programmable logic block provides to a carry chain multiplexer an output signal representing a partial output signal from a programmable lookup table (LUT), e.g., an output signal having a value that depends upon fewer than all of the data input signals of the LUT. In one embodiment, a first LUT output terminal provides a signal that depends upon fewer than all of the LUT data input signals, and the second LUT output terminal provides a signal that depends upon all of the LUT data input signals. In another embodiment, the first output signal depends upon X of the input signals and the second output signal depends upon Y of the input signals, X and Y being positive integers, X being less than Y. The first LUT output terminal drives a data input terminal, and the second LUT output terminal drives a select input terminal, of the carry chain multiplexer.