Rex Features
Syntax Era (working title) documents the rivalry between Armstrong's character, maverick visionary Sir Clive Sinclair, and his former colleague Chris Curry (Freeman) as they go head to head to achieve domination of the growing home computer market.
Other key cast members include Derek Riddell and Colin Michael Carmichael.
"Those of us that lived through the '80s will remember the sense of excitement when gadgets and technology started to appear in our homes, but not many of us will know the fascinating stories behind their arrival," said BBC Four controller Richard Klein.
"Alexander Armstrong and Martin Freeman are excellent choices to portray Sir Clive Sinclair and Chris Curry at a time when battling to have the UK's most loved home computer was their number one priority."
The 90-minute single drama, written by Tony Saint, is currently being filmed.
