Conway was born in Vallejo, California, on 24 July 1909, the son of Theodore Allen Barnewitz and Ruth Irene Quinn.

He enlisted in the Army as a private at the Presidio of San Francisco and in 1929 received an appointment to West Point from Richard J. Welch, 5th Congressional District, California.

His service included battalion and regimental command and duty as aide-de-camp to British General Sir Harold Alexander.

He was also one of the American officers who planned the Commando raid at Dieppe and participated as a shipboard observer on the British destroyer Alderney during that operation.

He served next with a NATO command, Allied Land Forces, Central Europe (ALFCE), with headquarters at Fontainebleau, France.

His final active-duty assignment followed his promotion to full general in the summer of 1966, when he served as commander-in-chief of the U.S. Strike Command, headquartered at MacDill Air Force Base near Tampa, Florida.

[2] Conway's decorations included the Legion of Merit with Oak Leaf Cluster; Bronze Star Medal with two Oak Leaf Clusters; French Legion of Honor; French Croix de Guerre with Palm; Czechoslovak Military Cross; Polish Golden Cross of Merit with Swords; Order of the British Empire; Order of the Crown of Italy; and the Army Distinguished Service Medal (US).

His Army remembrance recalls "a dedicated professional soldier, a man who truly 'filled the unforgiving minute with sixty seconds' worth of distance run.'

"[1] Beyond his many military and academic honors, Conway was especially proud of being one of the few members in the history of America's Armed Forces to have held both the lowest (Private) and highest (full General) regular ranks in the Army.