  We describe single-shot readout of a trapped-ion multi-qubit register using
space and time-resolved camera detection. For a single qubit we measure
0.9(3)x10^{-4} readout error in 400us exposure time, limited by the qubit's
decay lifetime. For a four-qubit register (a "qunybble") we measure an
additional error of only 0.1(1)x10^{-4} per qubit, despite the presence of 4%
optical cross-talk between neighbouring qubits. A study of the cross-talk
indicates that the method would scale with negligible loss of fidelity to
~10000 qubits at a density <~1 qubit/um^2, with a readout time ~1us/qubit.
