Except for a few analog computers used in special applications, all electronic computers today are digital. Digital computers were first experimented with during the late 1930s and early 1940s. They use binary numbers to represent numbers and characters and to perform calculations. Binary numbers consist of 0’s and 1’s and are therefore best suited to be handled by electronic circuits. For example, 0’s can be represented by a negative current and 1’s by a positive current.

George Stibitz, a mathematician at Bell Labs, was the first prominent experimenter to use binary numbers in a calculating device, although his device was electromechanical, and not electronic. In 1937 Stibitz built at his home a very simple adding device that could add two binary numbers. Subsequently, he built simple binary multipliers and dividers. Together with Sam Williams of Bell Labs he developed the complex calculator (also known as the Bell Telephone Lab Computer Model 1, or BTL Model 1). The calculator, completed at the end of 1939, contained 400 telephone relays. A teletype machine was used for data input and output. Two departments at Bell Labs that had to perform intensive calculations were connected to the BTL Model 1 via two remote teletype machines that functioned as computer terminals. In 1940 Stibitz linked the computer via telegraph lines to a terminal at Dartmouth College in New Hampshire, where mathematicians at a congress could enter calculations and receive a result a minute later.

Subsequently, Bell Labs developed several other calculators, of which the BLT Model V, completed in 1946, contained 9000 relays and weighed 10 tons. Its performance, considered very good at the time, was inferior to a present-day pocket calculator from a discount store: Multiplication of two seven-digit numbers took 1 second and their division 2.2 seconds.

In Germany, independently, Konrad Zuse, after having built a binary-number-based mechanical computer called Z1 in his parents’ sitting room, also used telephone relays in a computer called Z2. Both were built during the period 1936–39. A friend, Helmuth Schreyer, had proposed the use of vacuum tubes for switching elements, but because of the war conditions, vacuum tubes were difficult to obtain and Zuse used relays instead. The Z3, also based on electromechanical relays, was completed in 1941; it became the first universal computer that was controlled by a program. The Z3 was unreliable, however, and in 1944 Zuse replaced it with the Z4. The first three Zuse computers were destroyed by bombing during World War II and the fourth was a casualty of the disorder at the end of the war.

Although many engineers at that time preferred electric relays because they were more reliable than vacuum tubes, it was the vacuum tube that emerged victoriously from the decade 1940–50, mainly because of the tremendous speed at which logic circuits equipped with vacuum tubes could perform calculations. The theoretical physicist John V. Atanasoff and his assistant Clifford Berry had already completed a prototype of the vacuumtube- based computer in 1942. In many aspects the Atanasoff- Berry computer (ABC) reflected the design of modern electronic computers. It was primarily developed to solve systems of linear equations, but fell victim to World War II, which called Atanasoff and Berry to other projects.

In England, during the war years, M.H.A. Newman, T.H. Flowers, and Alan Turing and coworkers also developed a series of vacuum-tube computers. The overall name for these computers of 1940–44 was Colossus. Colossus was used for deciphering German messages that had been encoded using Enigma machines.