This presentation discusses two early computers on which David Wheeler worked. It first discusses the Electronic Delay Storage Automatic Calculator (EDSAC), which was the first practical stored-program electronic computer and which ran its first programs in 1949. In 1953, Wheeler designed an index register as an extension to the original EDSAC hardware. Wheeler also worked on the Titan computer, which later replaced EDSAC 2. Titan was the prototype of the Atlas 2 computer developed by Ferranti and the University of Cambridge Mathematical Laboratory. It was designed starting in 1963, and in operation from 1964 to 1973.