The most well-known tool for studying contextuality in quantum computation is the n-qubit Stabilizer state tableau representation. We provide an extension that not only describes the quantum state but is also outcome deterministic. The extension enables a value assignment to exponentially many Pauli observables, yet it remains quadratic in both memory and computational complexity. Furthermore, we show that the mechanisms employed for contextuality and measurement disturbance are wholly separate. The model will be useful for investigating the role of contextuality in n-qubit quantum computation.