Difference between revisions of "CSC103: DT's Notes 1"
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Furthermore, we know that a system where we only have two digits is called the binary system, and that this system is mathematically complete, allowing us to do everything we can do in decimal (we have concentrated in the previous discussion to just counting and adding, but we can do everything else the same). | Furthermore, we know that a system where we only have two digits is called the binary system, and that this system is mathematically complete, allowing us to do everything we can do in decimal (we have concentrated in the previous discussion to just counting and adding, but we can do everything else the same). | ||
| − | So the question now for engineers around the | + | So the question now for engineers around the middle of the 20th century was how to build electrical/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'''. | 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'''. | ||
| − | + | Many years later, Claude Shannon (1916-2001) showed in his Master's thesis that arithmetic operations on binary numbers could be performed using Boole's logic operators. In essence, if we map '''True''' and '''False''' to '''1''' and '''0''', adding two binary numbers can be done using logic operations. | |
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| + | We'll now look at Boole and Shannon separately. | ||
====Boole and the Boolean Algebra==== | ====Boole and the Boolean Algebra==== | ||
Revision as of 18:45, 31 January 2012
--© D. Thiebaut 08:10, 30 January 2012 (EST)
