Hoff gained his doctorate in 1962 at Stanford, where he worked for a further six years as a research associate. In 1968 he was invited by Robert Noyce to join his newly formed semiconductor firm, Intel.

Noyce had earlier shown how to assemble a large number of transistors into an integrated circuit (IC). Shortly after joining Intel, Hoff was asked to help some Japanese engineers design a number of IC chips to be used in desktop calculators.

Hoff proposed a calculator that could perform simple hardware instructions but could store complex sequences of these instructions in read-only memory (ROM) on a chip. The result of his idea was the first microprocessor – the Intel 4004 – released in 1971. Despite initial debate about its use and marketability, it became the forerunner of a whole range of advanced microprocessors, leading to a new generation of computers.

Hoff left Intel in 1982 to move to the computer company Atari to investigate new products. When Atari was sold in 1984 Hoff set up as an independent consultant.