Fano was born in Turin, Italy in 1917. He was known principally for his work on information theory, inventing (with Claude Shannon) Shannon–Fano coding and deriving the Fano inequality. He also invented the Fano algorithm and postulated the Fano metric. In the early 1960s, he was involved in the development of time-sharing computers, and from 1963 until 1968 served as founding director of MIT's Project MAC, which evolved to become what is now known as the MIT Computer Science and Artificial Intelligence Laboratory. Fano also helped to create MIT's original computer science curriculum. He retired from active teaching in 1984.
Fano's father was the mathematician Gino Fano, his older brother was physicist Ugo Fano, and his cousin was Giulio Racah. He grew up in Turin and studied engineering as an undergraduate at the School of Engineering of Torino (Politecnico di Torino) until 1939, when he emigrated to the United States as a result of anti-Jewish legislation passed under Benito Mussolini. He received his S.B. in electrical engineering from MIT in 1941, before joining the staff of the MIT Radiation Laboratory. After the war, he received an Sc.D., also from MIT, in 1947; his thesis, titled "Theoretical Limitations on the Broadband Matching of Arbitrary Impedances", was supervised by Ernst Guillemin. He joined the MIT faculty in 1947. Between 1950 and 1953, he led the Radar Techniques Group at Lincoln Laboratory. In 1954, Fano was made an IEEE Fellow for "contributions in the field of information theory and microwave filters".
Fano received the Claude E. Shannon Award in 1976 for his work in information theory. He died on 13 July 2016 at the age of 98.
In addition to his work in information theory, Fano also published articles and books about microwave systems, electromagnetism, network theory, and engineering education. His book-length publications include: