In the late 1960 NASA engineers were tasked with developing a digital flight computer that took up just one cubic foot of space on the Apollo 11 capsule and the software to guide the crew to the Moon. This TED-Ed video explains how it was done.
From YouTube:
The Apollo 11 moon landing was about the astronauts, mission control, software and hardware all working together as a seamless integrated system. None of which would have been possible without the contributions of one engineer: Margaret Hamilton. Who was this pioneer? Matt Porter and Margaret Hamilton detail how a woman and her team launched the software that took mankind to the Moon.