  The construction of a quantum computer remains a fundamental scientific and
technological challenge, in particular due to unavoidable noise. Quantum states
and operations can be protected from errors using protocols for fault-tolerant
quantum computing (FTQC). Here we present a step towards this by implementing a
quantum error correcting code, encoding one qubit in entangled states
distributed over 7 trapped-ion qubits. We demonstrate the capability of the
code to detect one bit flip, phase flip or a combined error of both, regardless
on which of the qubits they occur. Furthermore, we apply combinations of the
entire set of logical single-qubit Clifford gates on the encoded qubit to
explore its computational capabilities. The implemented 7-qubit code is the
first realization of a complete Calderbank-Shor-Steane (CSS) code and
constitutes a central building block for FTQC schemes based on concatenated
elementary quantum codes. It also represents the smallest fully functional
instance of the color code, opening a route towards topological FTQC.
