•The basis of the modern “Johnson” system that is still the most common today (Johnson & Morgan, 1951, Astrophysical Journal, 114, 522) is:
–A photometric criterion such that, measured OUTSIDE the atmosphere...
•For a normal A0V star:  (B-V)=(U-B)=0.0
•For a giant K0 (K0III) star: (B-V)=(U-B)=+1.0
–The spectral types were defined in the revised Yerkes system (Morgan, Keenan & Kellman, 1943, "An Atlas of Stellar Spectra with an Outline of Spectral Classification", Astrophysics Monographs, University of Chicago Press).
How the first system was defined...
All astronomical photometric systems have thus been defined by these simple equations:
1. For a white A0V star:  (B-V)=(U-B)=0.0
2. For a giant K0 (K0III) star: (B-V)=(U-B)=+1.0
3. 5 magnitudes difference is a factor of 100 in brightness.
4.Vega = magnitude 0.