Andrew Donald Booth was born on February 11, 1918, in East Molesy, Surrey, UK.

[2] From 1943 to 1945, Booth worked as a mathematical physicist in the X-ray team at the British Rubber Producers' Research Association (BRPRA), Welwyn Garden City, Hertfordshire, gaining his PhD in crystallography from the University of Birmingham in 1944.

In 1945, he moved to Birkbeck College, University of London, where his work in the crystallography group led him to build some of the first electronic computers in the United Kingdom[5][6] including the All Purpose Electronic Computer, first installed at the British Rayon Research Association.

[9] After World War II, he worked on crystallographic problems research at Birkbeck College and constructed a fourier synthesis device.

He was then introduced to the work of Alan Turing and John von Neumann on logical automata by Douglas Hartree.