I would imagine that the early Nintendo developed NES games from 1983 used the graph paper method, but a lot of the later games from the mid 80's onwards were created with much better tools and proper paint programs.
From about 1986 onward, an Amiga with Deluxe Paint was basically industry standard. So many game companies -- including Sega -- used it.
The manual for the version of Deluxe Paint I own (can't be bothered to go grab it at the moment) includes examples from Desert Strike in the manual when introducing you to the tools. Desert Strike was unreleased at the time. EA made both Deluxe Paint and Desert Strike.
Here's an example of sprite development for Super Mario Bros 3:
Most people were not drawing sprites by hand using binary calculations. That was basically limited to extremely tiny eastern european developers contracted out by US Gold to do shit ports of arcade titles to microcomputers in the span of weeks for dirt cheap, lol.
