A repetition code separates the logical value from the physical carriers by writing one value across several checked positions. The mapping is exact only for the declared code rule and ideal bit labels; real qubits add preparation error, leakage, correlated faults, decoherence, and readout uncertainty.
The first stabilizer habit is separating the logical value from the physical carriers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Logical one is copied into a checked word
The logical value 1 is encoded as the physical word 111.