Born in Hastings, Nebraska, Clarence L. Coates served in the U.S. Navy from 1944 to 1946. He first taught electrical engineering as an instructor at the University of Kansas at Lawrence where he earned his bachelor's and master's degrees. After completing his Ph.D. at the University of Illinois in 1953, he remained at the university as an assistant professor of electrical engineering and was promoted to associate professor in 1955.

Coates accepted a research scientist position at the General Electric Research Laboratory at Schenectady, New York, in 1956 and was named a senior research scientist in 1961. During this time period, he continued teaching as an adjunct professor at Rensselaer Polytechnic Institute.

In 1963 he joined the faculty of the University of Texas at Austin where he held many varied responsibilities. He served as a professor of computer sciences, supervised the graduate program in information sciences, and, for two years, chaired the department of electrical engineering. In 1967 he was named director of the Electronics Research Center and in 1968 assumed the additional responsibilities of supervisor of Engineering Computer Facilities. Returning to the midwest in 1971, he was a professor of electrical engineering at the University of Illinois at Urbana and directed the Coordinated Science Laboratory.

Coates came to Purdue in 1973 to head the School of Electrical Engineering and served as head for the next ten years. He emphasized computer education and the development of the computing facilities for the school. Recognizing the growing importance of the computer industry, he initiated a degree program in computer engineering. In 1983 he returned to teaching full-time in the computer area and retired from Purdue in 1988.

The holder of five patents, Coates is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and of the American Association for the Advancement of Science. He has held numerous offices in the IEEE and consulted extensively for organizations and universities. He is a member of Eta Kappa Nu, Phi Kappa Phi, Sigma Tau, Sigma Xi, and Tau Beta Pi.