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ENIAC's design and construction was financed by the United States Army, Ordnance Corps, Research and Development Command, led by Major General Gladeon M. Barnes. The total cost was about $487,000, equivalent to $7,051,000 in 2018. The construction contract was signed on June 5, 1943; work on the computer began in secret at the University of Pennsylvania's Moore School of Electrical Engineering the following month, under the code name "Project PX", with John Grist Brainerd as principal investigator. Herman H. Goldstine persuaded the Army to fund the project, which put him in charge to oversee it for them.

ENIAC was designed by John Mauchly and J. Presper Eckert of the University of Pennsylvania, U.S. The team of design engineers assisting the development included Robert F. Shaw (function tables), Jeffrey Chuan Chu (divider/square-rooter), Thomas Kite Sharpless (master programmer), Frank Mural (master programmer), Arthur Burks (multiplier), Harry Huskey (reader/printer) and Jack Davis (accumulators). In 1946, the researchers resigned from the University of Pennsylvania and formed the Eckert-Mauchly Computer Corporation.

By the end of its operation in 1956, ENIAC contained 20,000 vacuum tubes; 7,200 crystal diodes; 1,500 relays; 70,000 resistors; 10,000 capacitors; and approximately 5,000,000 hand-soldered joints. It weighed more than 30 short tons (27 t), was roughly 2.4 m x 0.9 m x 30 m (8 ft x 3 ft x 98 ft) in size, occupied 167 m2 (1,800 sq ft) and consumed 150 kW of electricity. This power requirement led to the rumor that whenever the computer was switched on, lights in Philadelphia dimmed. Input was possible from an IBM card reader and an IBM card punch was used for output. These cards could be used to produce printed output offline using an IBM accounting machine, such as the IBM 405. While ENIAC had no system to store memory in its inception, these punch cards could be used for external memory storage. In 1953, a 100-word magnetic-core memory built by the Burroughs Corporation was added to ENIAC.

ENIAC used ten-position ring counters to store digits; each digit required 36 vacuum tubes, 10 of which were the dual triodes making up the flip-flops of the ring counter. Arithmetic was performed by "counting" pulses with the ring counters and generating carry pulses if the counter "wrapped around", the idea being to electronically emulate the operation of the digit wheels of a mechanical adding machine.

It was possible to wire the carry of one accumulator into another accumulator to perform double precision arithmetic, but the accumulator carry circuit timing prevented the wiring of three or more for even higher precision. ENIAC used four of the accumulators (controlled by a special multiplier unit) to perform up to 385 multiplication operations per second; five of the accumulators were controlled by a special divider/square-rooter unit to perform up to 40 division operations per second or three square root operations per second.

The other nine units in ENIAC were the initiating unit (started and stopped the machine), the cycling unit (used for synchronizing the other units), the master programmer (controlled loop sequencing), the reader (controlled an IBM punch-card reader), the printer (controlled an IBM card punch), the constant transmitter, and three function tables.

The basic machine cycle was 200 microseconds (20 cycles of the 100 kHz clock in the cycling unit), or 5,000 cycles per second for operations on the 10-digit numbers. In one of these cycles, ENIAC could write a number to a register, read a number from a register, or add/subtract two numbers.

ENIAC used common octal-base radio tubes of the day; the decimal accumulators were made of 6SN7 flip-flops, while 6L7s, 6SJ7s, 6SA7s and 6AC7s were used in logic functions. Numerous 6L6s and 6V6s served as line drivers to drive pulses through cables between rack assemblies.

Several tubes burned out almost every day, leaving ENIAC nonfunctional about half the time. Special high-reliability tubes were not available until 1948. Most of these failures, however, occurred during the warm-up and cool-down periods, when the tube heaters and cathodes were under the most thermal stress. Engineers reduced ENIAC's tube failures to the more acceptable rate of one tube every two days. According to an interview in 1989 with Eckert, "We had a tube fail about every two days and we could locate the problem within 15 minutes." In 1954, the longest continuous period of operation without a failure was 116 hoursóclose to five days.