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Boole, George

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British Mathematician 1815–1864

Digital logic is the set of rules applied to data (numbers, symbols, words) that are entered into a computer. These instructions direct computers and are called machine code. This code uses the binary digits 1 and 0 to switch transistors on or off. The basic operators that perform these tasks are AND, OR, and NOT. A hundred years before electronic computers were conceived, George Boole proposed this binary or digital logic.

Born to working-class English parents, Boole later supported himself and his parents as a school instructor. Frustrated by the inferior mathematics texts used to educate pupils, Boole was led to change the world of numbers. With only a basic science background, Boole labored 5 years to learn mathematics, eventually publishing in the Cambridge Mathematical Journal. His reputation was heightened in 1847 when he published The Mathematical Analysis of Logic, which introduced Boole's ideas on the two-valued (presence "1" or absence "0") system of algebra that represented logical operations.

For centuries, philosophers have studied logic. However, George Boole argued that logic could be taught with mathematics rather than with philosophy. Boole envisioned mathematical symbols, rather than words, as the truest representation of logic.

Even though he had not studied at a university, Boole was appointed in 1849 as mathematics professor at Queens (University) College in Ireland. Eventually, Boole was appointed to the position of mathematics chairman at Queens, where he gained a reputation as an outstanding teacher.

In 1854, Boole published An Investigation into the Laws of Thought, in which he combined algebra with logic. This concept became known as Boolean algebra. Because George Boole demonstrated that logic could be reduced to very simple algebraic systems, it was possible for Charles Babbage and his successors to design mechanical devices that could perform the necessary logical tasks. Today, Boolean algebra is the logic that computers use to perform everything they do.

Boolean Algebra

Boolean algebra is a branch of mathematics in which statements, ideas, numbers, and so forth are denoted by symbols (e.g., x, y, z) and can be acted upon by operators (e.g., AND or OR). The operator AND between two symbols (x AND y) is known as the union of x and y and refers to objects both in x and y. The operator OR represents the intersection of x and y (x OR y) and consists of objects either in x, in y, or in both x and y.

As an example of applying Boolean algebra in computers, let x and y denote two electronic circuits that are either closed (electricity flows) or open (electricity does not flow). The statement x AND y is represented by connecting the switches in series. (See series diagram.) The current will flow only if both x and y are closed. Similarly, a circuit with switches connected in parallel is represented by the statement x OR y. (See parallel diagram.) The current will flow if either x is closed, y is closed, or both x and y are closed.

Internet search engines use Boolean algebra in the form of AND and OR. For instance, searching "African OR American" produces articles that contain either or both these words, a result that is broad in scope. Searching for "African AND American" produces articles that contain both words, a result that is more narrow in scope.

Boole's Influence on Computers

Boole was a great mathematician, but he never forgot that mathematics came into existence to search for practical scientific solutions. Boolean algebra is the basis for subjects such as information theory, computer science, electrical-circuit theory, and artificial-intelligence research.

Seventy-three years after Boole's death, an MIT student recognized the connection between electronic circuits and Boolean algebra. The student transferred two logic states to electronic circuits by assigning different voltage levels to each state. This connection was the step necessary to take Boole's theory to the practical design of computers. As a result, Boole is considered one of the founding fathers of computers and information technology.

SEE ALSO BABBAGE, CHARLES; COMPUTERS, EVOLUTION OF ELECTRONIC; MATHEMATICAL DEVICES, EARLY; MATHEMATICAL DEVICES, MECHANICAL.

William Arthur Atkins with

Philip Edward Koth

Bibliography

Boole, George. An Investigation of the Laws of Thought. New York: Dover Publications, 1958.

Boyer, Carl B. A History of Mathematics, 2nd ed. New York: John Wiley and Sons, Inc., 1991.

Henderson, Harry. Modern Mathematicians. New York: Facts on File, 1996.

Internet Resources

"George Boole." School of Mathematics and Statistics, University of St Andrews, Scotland. <http://www.history.mcs.st-and.ac.uk/history/Mathematicians/Boole.html>.