【F1】
Computer science as an independent discipline dates to only about 1960, although the electronic digital computer that is the object of its study was invented some two decades earlier.
The roots of computer science lie primarily in the related fields of electrical engineering and mathematics. Electrical engineering provides the basics of circuit design—namely, the idea that electrical impulses input to a circuit can be combined to produce arbitrary outputs.【F2】
The invention of the transistor and the miniaturization of circuits, along with the invention of electronic, magnetic, and optical media for the storage of information, resulted from advances in electrical engineering and physics.
Mathematics is the source of one of the key concepts in the development of the computer—the idea that all information can be represented as sequences of zeros and ones. In the binary number system, numbers are represented by a sequence of the binary digits 0 and 1 in the same way that numbers in the familiar decimal system are represented using the digits 0 through 9.【F3】
The relative ease with which two states(e. g. , high and low voltage)can be realized in electrical and electronic devices led naturally to the binary digit, or bit, becoming the basic unit of data storage and transmission in a computer system.
The Boolean algebra developed in the 19th century supplied a formalism for designing a circuit with input values of 0"s and 1 "s(false or true, respectively, in the terminology of logic)to yield any desired combination of 0" s and l"s as output.【F4】
Theoretical work on computability, which began in the 1930s, provided the needed extension to the design of whole machines; a milestone was the 1936 specification of the conceptual Turing machine(a theoretical device that manipulates an infinite string of 0" s and 1" s)by the British mathematician Alan Turing and his proof of the model"s computational power.
Another breakthrough was the concept of the stored-program computer, usually credited to the German-American mathematician John von Neumann.【F5】
This idea—that instructions as well as data should be stored in the computer"s memory for fast access and execution—was critical to the development of the modern computer. Previous thinking was limited to the calculator approach, in which instructions are entered one at a time.