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LECTURE 12 (full)

# LECTURE 12 (full) - LECTURE 12 LECTURE 12 DIGITAL SYSTEMS...

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CTURE 2 LECTURE 12. DIGITAL SYSTEMS structor: Prof. kyu ark Instructor: Prof. Inkyu Park Department of Mechanical Engineering Korea Advanced Institute of Science and Technology (KAIST) MAE307 Applied Electronics © Inkyu Park, 2010

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Review of Lecture 11 MAE307 Applied Electronics © Inkyu Park, 2010
Analog vs. Digital Signals Analog Signal A signal that has a continuous Digital Signal A signal in which discrete steps are nature rather than a pulsed or discrete nature. used to represent the information. “Quantization” MAE307 Applied Electronics © Inkyu Park, 2010

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Boolean Algebra A logical calculus of truth values developed by George Boole. Terminologies: - Boolean variables : 0 (false) and 1 (true). -Logic functions : functions of logical (boolean) variables that can be carried out in terms of truth tables. - Truth tables : a listing of all the possible values that each of the boolean variables can take & of the corresponding value of the desired function. MAE307 Applied Electronics © Inkyu Park, 2010 -Log ic ga tes : physical devices that can be used to implement logic functions.
AND, OR, and NOT Gates AND Gate OR Gate NOT Gate 0 · 0 = 0 · 1 = 0 Logical Multiplication 0 + 0 = 0 +1 = 1 Logical Addition Logical Inversion (Complement) 0=1 0 1 0 1 · 0 = 0 1 · 1 = 1 0 + 1 1 1 + 0 = 1 1 + 1 = 1 ~ 0 = 1 ~ 1 = 0 0 1 1 MAE307 Applied Electronics © Inkyu Park, 2010 1

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Basic Rules for Boolean Algebra MAE307 Applied Electronics © Inkyu Park, 2010
NAND and NOR Gates NAND Gate : Logical Inversion on the Multiplication = Logical Addition on the Complement NOR Gate : Logical Inversion on the Addition = Logical Multiplication on the Complement MAE307 Applied Electronics © Inkyu Park, 2010

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XOR Gate     Y X Y X Z MAE307 Applied Electronics © Inkyu Park, 2010
Half Adder Realize the summation of two binary numbers. S represents the summation result. represents the carry (to higher digit) AB S C C represents the carry (to higher digit). (sum) (carry) 00 0 0 0 1 1 0 10 1 0 1 1 0 1 B A B A S B A C MAE307 Applied Electronics © Inkyu Park, 2010

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Karnaugh Maps for Logic Design : Example (I) Given: Truth table for y(A,B,C,D). Find: Realization of y (i.e. logic circuit design). How can we design the logic circuit to alize this logic realize this logic function? MAE307 Applied Electronics © Inkyu Park, 2010
Karnaugh Maps for Logic Design : Example (I) First, construct the Karnaugh map & find the simple logic expression. Two-cube subcell D B A our- be bcells Four cube subcells D A C B D C Logic expression: MAE307 Applied Electronics © Inkyu Park, 2010 D C D A C B D B A y

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Karnaugh Maps for Logic Design : Example (I) We can construct the logic circuit from the simplified logic function. D C D A C B D B A y MAE307 Applied Electronics © Inkyu Park, 2010
Outline Sequential Logic Modules - Flip-Flops (RS, D, JK, T flip-flops) igital Counters - Digital Counters -Reg is ters Sequential Logic Design - Flip-Flops (RS, D, JK, T flip-flops) - Digital Counters Microprocessors Microcontrollers MAE307 Applied Electronics © Inkyu Park, 2010

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LECTURE 12 (full) - LECTURE 12 LECTURE 12 DIGITAL SYSTEMS...

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