Integrated circuits with programmable logic regions are provided. The programmable logic regions may be organized into smaller logic units sometimes referred to as a logic element. A logic element may include four lookup tables coupled to an adder carry chain. At least some of the lookup tables are configured to output combinatorial outputs, whereas the adder carry chain are used to output sum outputs. Both the combinatorial outputs and the sum outputs may be used simultaneously to support a multiplication operation, three or more logic operations, or arithmetic and combinatorial operations in parallel.