The document outlines the fundamentals of computer circuit logic gates and Boolean logic, explaining their history, types, and applications. It covers basic gates like AND, OR, NOT, as well as combination gates such as NAND, NOR, XOR, and XNOR, demonstrating their operations and truth tables. Additionally, the document emphasizes the role of Boolean algebra in simplifying and analyzing digital circuits.

1. Computer Circuit Logic GateWith Boolean LogicYinong WangYoungik SongApril 18th 2011

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

17. Boolean Example

18. Boolean Example

19. Boolean Example

20. Actual Products of Logic Gate

21. Summary and ConclusionAll digital equipment is constructed using a few logic gate.

22. The basic logic gates are AND, OR, NOT gate.

23. Combination logic gates are NAND, NOR, XOR, XNOR gate.