Difference between revisions of "CSC103: DT's Notes 1"
| Line 340: | Line 340: | ||
So the question now for engineers around the mid 20th century is how to build electronic circuits that would perform arithmetic. | So the question now for engineers around the mid 20th century is how to build electronic circuits that would perform arithmetic. | ||
| + | The answer to this problem is provided by two giants of computer science, '''George Boole''', and '''Claude Shannon''' who lived at very different times, but provided two complementary parts of the solution. Boole (1815-1864) defined the ''Boolean algebra'', a logic system that borrowed from philosophy and from mathematics, where assertions (mathematicians say ''variables'') can only be ''true''' or '''false''', and where assertions can be combined by any combination of three conjunctions (which mathematicians call ''operators''): '''and''', '''or''' and '''not'''. | ||
| − | + | About seventy years after Boole's death, Claude Shannon (1916-2001) while attending a philosophy class at the University of Michigan came across Boole's work and recognized that this could be the solution to making electrical/electronic calculators. In 1937 Shannon started work on a Master's thesis at MIT and showed that all arithmetic operations in binary could be implemented using Boole's logic operators. In other words, one could add 1s and 0s by treating them as false or true statements and combining them with '''and''', '''or''' and '''not''' operators. | |
| + | ====Boole and the Boolean Algebra==== | ||
| − | + | Boole's contribution is a major one in the history of computers. In the 1840s, he conceived of a mathematical world where there would be only two symbols, two values, and three operations that could be performed with them, and he proved that such a system could exhibit the same rules exhibited by an algebra. The two values used by Boole's algebra are ''True'' and ''False'', or ''T'' and ''F'', and the operators are ''and'', ''or'' and ''not''. Boole was in fact interested in logic, and expressing combinations of statements that can either be true or false, and figuring out whether mathematics could be helpful in formulating a logic system where we could express any logical expression containing multiple simple statements that could be either true or false. | |
| − | |||
| − | Boole's contribution | ||
While this seems something more interesting to philosophers than mathematicians or engineers, this system is the foundation of modern electronic computers. | While this seems something more interesting to philosophers than mathematicians or engineers, this system is the foundation of modern electronic computers. | ||
Revision as of 18:34, 31 January 2012
--© D. Thiebaut 08:10, 30 January 2012 (EST)
