In this work we report an improved experimental determination of K-shell binding energies from Be-like ${\mathrm{Ne}}^{6+}$, B-like ${\mathrm{Ne}}^{5+}$, and C-like ${\mathrm{Ne}}^{4+}$ ground-state multiply charged ions using high- resolution Ne-K Auger-electron spectroscopy. The derived energy differences, namely, ${\mathrm{Ne}}^{6+}$ E(1${\mathit{s}}^{2}$2${\mathit{s}}^{2}$) $^{1}$S--${\mathrm{Ne}}^{7+}$ E(1s2${\mathit{s}}^{2}$${)}^{2}$S, ${\mathrm{Ne}}^{5+}$ E(1${\mathit{s}}^{2}$2${\mathit{s}}^{2}$2p) $^{2}$P\ifmmode^\circ\else\textdegree\fi{}--${\mathrm{Ne}}^{6+}$ E(1s2${\mathit{s}}^{2}$2p) $^{3}$P\ifmmode^\circ\else\textdegree\fi{}, and ${\mathrm{Ne}}^{4+}$ E(1${\mathit{s}}^{2}$2${\mathit{s}}^{2}$2${\mathit{p}}^{2}$) $^{3}$P--${\mathrm{Ne}}^{5+}$ E(1s2${\mathit{s}}^{2}$2${\mathit{p}}^{2}$${(}^{3}$P)) $^{4}$P are 1099.1, 1048.5, and 1001.8 eV, respectively. These energies are accurate to within \ifmmode\pm\else\textpm\fi{}0.1 eV. Theoretically, we have studied relativistic binding energies of ${\mathrm{Ne}}^{\mathit{q}+}$ (q=6, 5, and 4) by using the (i) saddle-point technique, (ii) 1/Z method, and (iii) multiconfiguration Dirac-Fock model. Excellent agreement with experiment is obtained.