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Computer Circuit Logic GateWith Boolean Logic Yinong Wang Youngik Song April 18th 2011
Table of Contents Introduction History of Logic Gate and Boolean Logic Basic Logic Gate Inverting Logic Gate Application of Logic Gate Boolean Algebra Rules Boolean Example Actual Products of Logic Gates Summary and Conclusion References
Introduction All 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 – 0 The 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’.
History of Logic Gate and Boolean Logic 1847 – 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.
Basic Logic Gates ,[object Object],It has two or more input and a single output. Boolean Logic Y = AB  or Y = A·B Logic Symbol Series Circuit Truth Table Electronic Circuit
Basic logic gates ,[object Object],     It has two or more input and a single output. Boolean Logic Y = A + B Logic Symbol Parallel Circuit Truth Table Electronic Circuit
Inverting logic gates ,[object Object],  It is the simplest logic gate. It has only one   input and one output.  Logic Symbol Boolean Logic A = Ā Truth Table Electronic Circuit
Inverting logic gates ,[object Object],It is a combination of NOT gate and AND gate Y Boolean Logic Y = AB  or Y = A·B Truth Table Logic Symbol
Inverting logic gates ,[object Object],It is a combination of NOT gate and OR gate Y Boolean Logic Y = A + B Y Truth Table Logic Symbol
Application of Logic Gate ,[object Object],When the inputs are opposite, the output is a HIGH. Y Boolean Logic Y = AB + AB Truth Table Y Boolean Logic Y = A + B Logic Symbol
Application of Logic Gate ,[object Object],When the inputs are opposite, the output is a LOW. Y Boolean Logic Y = AB + AB Truth Table Y Boolean Logic Y = A + B Logic Symbol
Application of Logic Gate ,[object Object],A decoder is a circuit that looks at its inputs and determines which binary number is represented by this input Truth Table
Application of Logic Gate ,[object Object],Encoders are opposite of decoder. An encoder takes one input and generates a multi-bit output code. Truth Table
Application of Logic Gate ,[object Object],The 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.
Boolean Algebra Rules  ,[object Object],                A+B=B+A                 A·B=B·A ,[object Object],A+(B+C)=(A+B)+C ,[object Object],             A·(B+C)=(A·B)+(A·C) ,[object Object],          A = A
Boolean Algebra Rules ,[object Object],A+0=A           A+A=A             A+1=1            A+Ā=1 ,[object Object],A·0=0            A·1= A             A·A=A            A·Ā=0  ,[object Object],A·B= A+B             A + B = A·B
Boolean Example
Boolean Example
Boolean Example
Actual Products of Logic Gate
Summary and Conclusion ,[object Object]
The basic logic gates are AND, OR, NOT gate.
Combination logic gates are NAND, NOR, XOR, XNOR gate.

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Computer circuit logic

  • 1. Computer Circuit Logic GateWith Boolean Logic Yinong Wang Youngik Song April 18th 2011
  • 2. Table of Contents Introduction History of Logic Gate and Boolean Logic Basic Logic Gate Inverting Logic Gate Application of Logic Gate Boolean Algebra Rules Boolean Example Actual Products of Logic Gates Summary and Conclusion References
  • 3. Introduction All 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 – 0 The 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 Logic 1847 – 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.
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  • 20. Actual Products of Logic Gate
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  • 22. The basic logic gates are AND, OR, NOT gate.
  • 23. Combination logic gates are NAND, NOR, XOR, XNOR gate.
  • 24. Using logic gate can be made an affordable circuits such as an encoder, a decoder, memory circuits.
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  • 26. Thank you for watching our presentationAny questions ?