Computer circuit logic
- 2. Table of ContentsIntroductionHistory of Logic Gate and Boolean LogicBasic Logic GateInverting Logic GateApplication of Logic GateBoolean Algebra RulesBoolean ExampleActual Products of Logic GatesSummary and ConclusionReferences
- 3. IntroductionAll digital equipment is constructed using a few basic circuit.The basic logic element is called a gate.All logic gate has input and output.High - ON – 1 Low - OFF – 0The gate looks at its input and based on their state and its operation.The gate generates the appropriate output reflecting the decision it has made.Boolean logic or Boolean algebra is a logical calculus which has only two value, ‘true’ or ‘false’.
- 4. History of Logic Gate and Boolean Logic1847 – George Boole (1815-1864) published, ‘The Mathematical Analysis of Logic’.1898 – Nikola Tesla filed for patents of devices containing logic gate circuits. Vacuum tubes replaced relays for logic operations.1907 – Lee De Forest’s modification of the Fleming valve can be used as AND logic gate.1924 – Walther Bothe invented the first modern electronic AND gate.1937 – Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switching circuit.
- 5. Basic Logic GatesAND GATE It has two or more input and a single output.Boolean LogicY = AB or Y = A·BLogic SymbolSeries CircuitTruth TableElectronic Circuit
- 6. Basic logic gates OR GATE It has two or more input and a single output.Boolean LogicY = A + BLogic SymbolParallel CircuitTruth TableElectronic Circuit
- 7. Inverting logic gatesNOT GATE It is the simplest logic gate. It has only one input and one output. Logic SymbolBoolean LogicA = ĀTruth TableElectronic Circuit
- 8. Inverting logic gatesNAND GATEIt is a combination of NOT gate and AND gateYBoolean LogicY = AB or Y = A·BTruth TableLogic Symbol
- 9. Inverting logic gatesNOR GATEIt is a combination of NOT gate and OR gateYBoolean LogicY = A + BYTruth TableLogic Symbol
- 10. Application of Logic GateXOR (Exclusive OR) GATEWhen the inputs are opposite, the output is a HIGH.YBoolean LogicY = AB + ABTruth TableYBoolean LogicY = A + BLogic Symbol
- 11. Application of Logic GateXNOR (Exclusive NOR) GATEWhen the inputs are opposite, the output is a LOW.YBoolean LogicY = AB + ABTruth TableYBoolean LogicY = A + BLogic Symbol
- 12. Application of Logic GateDECODERA decoder is a circuit that looks at its inputs and determines which binary number is represented by this inputTruth Table
- 13. Application of Logic GateENCODEREncoders are opposite of decoder. An encoder takes one input and generates a multi-bit output code.Truth Table
- 14. Application of Logic GateFlip FlopThe flip-flop is the basic element for a memory circuit. It is comprised of an assembly of logic gates to permit information to be stored.
- 15. Boolean Algebra Rules Commutative law A+B=B+A A·B=B·AAssociative lawA+(B+C)=(A+B)+CDistributive law A·(B+C)=(A·B)+(A·C) Double-Inversion Rule A = A
- 16. Boolean Algebra RulesOR Gate RulesA+0=A A+A=A A+1=1 A+Ā=1AND Gate RulesA·0=0 A·1= A A·A=A A·Ā=0 DeMorgan’s TheoremsA·B= A+B A + B = A·B
- 24. Using logic gate can be made an affordable circuits such as an encoder, a decoder, memory circuits.
- 25. Boolean algebra can be determined logic gates and simplified them, so this logic is an important tool used in many of digital circuit.ReferencesHistory of logic gate.http://en.wikipedia.org/wiki/Logic_gate#History_and_developmentHistory of Boolean logic and ruleshttp://www.buzzle.com/articles/boolean-origination-history-and-origin-of-boolean-logic.htmlLogic gates introduction and examplesThe website of Mario Ulcar -> Tutorials-> Digitalhttp://faculty.georgebrown.ca/~mulcar/