What is the chemical formula for the binary compound nitrogen dioxide?

NO2

The compound, nitrogen(IV) oxide, is a radical species as written (it has 17 valence electrons), and participates in the following equilibrium:

2NO2(g)⇌N2O4(g)

The dimer is colourless, and contains a N−N bond presumed to derive from the coupling of the lone electrons on the 2 nitrogen centres; the radical species red brown.

Note that the attempt to represent the Lewis structures of these species invariably involves charge separation and FORMAL positive and negative charges on, respectively, nitrogen and oxygen. This is 1st year/2nd year inorganic chemistry rather than A level.