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# Computer circuit logic

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Computer circuit logic and Boolean logic include basic logic gate (AND,OR,NOT,NAND,NOR) and some examples.

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### Computer circuit logic

1. 1. Computer Circuit Logic GateWith Boolean Logic<br />Yinong Wang<br />Youngik Song<br />April 18th 2011<br />
2. 2. Table of Contents<br />Introduction<br />History of Logic Gate and Boolean Logic<br />Basic Logic Gate<br />Inverting Logic Gate<br />Application of Logic Gate<br />Boolean Algebra Rules<br />Boolean Example<br />Actual Products of Logic Gates<br />Summary and Conclusion<br />References<br />
3. 3. Introduction<br />All digital equipment is constructed using a few basic circuit.<br />The basic logic element is called a gate.<br />All logic gate has input and output.<br />High - ON – 1 Low - OFF – 0<br />The gate looks at its input and based on their state and its operation.<br />The gate generates the appropriate output reflecting the decision it has made.<br />Boolean logic or Boolean algebra is a logical calculus which has only two value, ‘true’ or ‘false’.<br />
4. 4. History of Logic Gate and Boolean Logic<br />1847 – George Boole (1815-1864) published, ‘The Mathematical Analysis of Logic’.<br />1898 – Nikola Tesla filed for patents of devices containing logic gate circuits. Vacuum tubes replaced relays for logic operations.<br />1907 – Lee De Forest’s modification of the Fleming valve can be used as AND logic gate.<br />1924 – Walther Bothe invented the first modern electronic AND gate.<br />1937 – Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switching circuit.<br />
5. 5. Basic Logic Gates<br /><ul><li>AND GATE </li></ul>It has two or more input and a single output.<br />Boolean Logic<br />Y = AB or Y = A·B<br />Logic Symbol<br />Series Circuit<br />Truth Table<br />Electronic Circuit<br />
6. 6. Basic logic gates<br /><ul><li> OR GATE</li></ul> It has two or more input and a single output.<br />Boolean Logic<br />Y = A + B<br />Logic Symbol<br />Parallel Circuit<br />Truth Table<br />Electronic Circuit<br />
7. 7. Inverting logic gates<br /><ul><li>NOT GATE </li></ul> It is the simplest logic gate. It has only one<br /> input and one output. <br />Logic Symbol<br />Boolean Logic<br />A = Ā<br />Truth Table<br />Electronic Circuit<br />
8. 8. Inverting logic gates<br /><ul><li>NAND GATE</li></ul>It is a combination of NOT gate and AND gate<br />Y<br />Boolean Logic<br />Y = AB or Y = A·B<br />Truth Table<br />Logic Symbol<br />
9. 9. Inverting logic gates<br /><ul><li>NOR GATE</li></ul>It is a combination of NOT gate and OR gate<br />Y<br />Boolean Logic<br />Y = A + B<br />Y<br />Truth Table<br />Logic Symbol<br />
10. 10. Application of Logic Gate<br /><ul><li>XOR (Exclusive OR) GATE</li></ul>When the inputs are opposite, the output is a HIGH.<br />Y<br />Boolean Logic<br />Y = AB + AB<br />Truth Table<br />Y<br />Boolean Logic<br />Y = A + B<br />Logic Symbol<br />
11. 11. Application of Logic Gate<br /><ul><li>XNOR (Exclusive NOR) GATE</li></ul>When the inputs are opposite, the output is a LOW.<br />Y<br />Boolean Logic<br />Y = AB + AB<br />Truth Table<br />Y<br />Boolean Logic<br />Y = A + B<br />Logic Symbol<br />
12. 12. Application of Logic Gate<br /><ul><li>DECODER</li></ul>A decoder is a circuit that looks at its inputs and determines which binary number is represented by this input<br />Truth Table<br />
13. 13. Application of Logic Gate<br /><ul><li>ENCODER</li></ul>Encoders are opposite of decoder. An encoder takes one input and generates a multi-bit output code.<br />Truth Table<br />
14. 14. Application of Logic Gate<br /><ul><li>Flip Flop</li></ul>The flip-flop is the basic element for a memory circuit. <br />It is comprised of an assembly of logic gates to permit information to be stored.<br />
15. 15. Boolean Algebra Rules <br /><ul><li>Commutative law</li></ul> A+B=B+A<br /> A·B=B·A<br /><ul><li>Associative law</li></ul>A+(B+C)=(A+B)+C<br /><ul><li>Distributive law</li></ul> A·(B+C)=(A·B)+(A·C)<br /><ul><li> Double-Inversion Rule</li></ul> A = A<br />
16. 16. Boolean Algebra Rules<br /><ul><li>OR Gate Rules</li></ul>A+0=A A+A=A<br /> A+1=1 A+Ā=1<br /><ul><li>AND Gate Rules</li></ul>A·0=0 A·1= A<br /> A·A=A A·Ā=0 <br /><ul><li>DeMorgan’s Theorems</li></ul>A·B= A+B A + B = A·B<br />
17. 17. Boolean Example<br />
18. 18. Boolean Example<br />
19. 19. Boolean Example<br />
20. 20. Actual Products of Logic Gate<br />
21. 21. Summary and Conclusion<br /><ul><li>All digital equipment is constructed using a few logic gate.
22. 22. The basic logic gates are AND, OR, NOT gate.
23. 23. Combination logic gates are NAND, NOR, XOR, XNOR gate.
24. 24. Using logic gate can be made an affordable circuits such as an encoder, a decoder, memory circuits.
25. 25. Boolean algebra can be determined logic gates and simplified them, so this logic is an important tool used in many of digital circuit.</li></li></ul><li>References<br /><ul><li>History of logic gate.</li></ul>http://en.wikipedia.org/wiki/Logic_gate#History_and_development<br /><ul><li>History of Boolean logic and rules</li></ul>http://www.buzzle.com/articles/boolean-origination-history-and-origin-of-boolean-logic.html<br /><ul><li>Logic gates introduction and examples</li></ul>The website of Mario Ulcar -> Tutorials-> Digital<br />http://faculty.georgebrown.ca/~mulcar/<br />
26. 26. Thank you for watching our presentationAny questions ?<br />