This paper considers a test set for an ALU with look ahead carry generators(LCGs). The ALU is logically partitioned into two groups of blocks, the group of one-bit operation units and LCG group. Each group is tested in parallel and exhaustively, independent of the other. And an easily testable design is applied to several blocks for decreasing the number of the input combinations of them. Under the easily testable design, a minimum test set for each group is generated, and the upper and lower bounds for a minimum test for the ALU are derived. The difference of the lower and upper bounds is not large, and a test set whose number of test vectors is equal to the upper bound can be easily obtained as the union of minimum test sets for two groups. Hence, the union can be used as a complete and practical test set for the ALU.