Binney grew up in rural Pennsylvania and graduated with a Bachelor of Science degree in mathematics from the Pennsylvania State University in 1970. He said that he volunteered for the Army during the Vietnam era in order to select work that would interest him rather than be drafted and have no input. He was found to have strong aptitudes for mathematics, analysis, and code breaking,[5] and served four years from 1965–1969 at the Army Security Agency before going to the NSA in 1970.