Difference between revisions of "CSC103: DT's Notes 2"
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| + | We saw last week the importance of Boole and Shannon for the field of computer science. | ||
| + | What Shannon gave us is the ability to look at binary arithmetic as a logical process. When we add two bits together, we get two new bits as a result. One that is the '''sum''' and one that is the '''carry''' bit that is fed to the next column, the one on the left, when adding by hand. Refer to the page for [[CSC103:_DT%27s_Notes_1 | Week 1]] if you need to refresh your memory. | ||
| + | We name the two bits we're adding '''a''' and '''b''', for convenience. We call the ''sum'' bit '''S''', and the ''carry'' bit '''C'''. | ||
| + | The logic equations for '''S''' and '''C''' become: | ||
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| + | ::'''S''' = ( '''a''' ''and'' ''not'' '''b''' ) ''or'' ( ''not'' '''a''' ''and'' '''b''' ) | ||
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| + | ::'''C''' = '''a''' and '''b''' | ||
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| + | [[Image:CSC103ElectricalAndOrCircuits.png|200px|right]] Our ability to define the addition of two binary numbers in terms of logic operations with the operators '''and''', '''or''' and '''not''' is of tremendous importance. Remember that by the time Shannon released his Master's thesis, engineers knew how to efficiently and simply create electrical circuits that could implement the three elementary operators, as illustrated in the diagram to the right. Here we have shown simple circuits that use switches, but this could be done just as simply (for an electronics engineer) using relays, vacuum tubes, or transistors. | ||
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| + | So that's what they just did. They started making simple electronic circuits that worked with a low voltage (5 Volts) and contained several AND circuits, or OR circuits, or NOT circuits. | ||
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| + | Below is a picture of such a circuit, with the ''schematics'' of the four '''And''' ''gates'', or '''And''' circuits one would find inside. | ||
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| + | <center>[[Image:74LS08AndDime.png|400px]]</center> | ||
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| + | Engineers gave each circuit a different shape depending on which logic function they | ||
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Latest revision as of 16:26, 6 February 2012
--D. Thiebaut 15:07, 6 February 2012 (EST)
