We propose a new measurement theory, in qubits handling, based on the truth values, i.e., the truth T (1) for true and the falsity F (0) for false. The results of measurement are either 0 or 1. To implement Deutsch's algorithm, we need both observability and controllability of a quantum state. The new measurement theory can satisfy these two. Especially, we systematically describe our assertion based on more mathematical analysis using raw data in a thoughtful experiment