# Hw4 - Department of Systems Engineering and Engineering Management ERG 2020 C/D Digital Logic and Systems Instruction Question 1 THE CHINESE

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Unformatted text preview: Department of Systems Engineering and Engineering Management ERG 2020 C/D Digital Logic and Systems Instruction: Question 1. THE CHINESE UNIVERSITY OF HONG KONG Show your work clearly. Assignment 4 Prove by Switching Algebra that ( + ) ( + )= X Y X 0 Z X 0 Z + T X 0 Y You may assume that theorems ( 1){( 11) and ( 1 ){ (11 ) are true. T T T 0 Question 2. Write the truth table for the following logic function: F =( W X )( +) 0 Y 0 Z 0 0 Question 3. Write the canonical sum and product for the following logic function: F = X + Y 0 Z 0 Question 4. Using Karnaugh map, nd a minimal sum-of-products expression for the following logic function. Indicate the distinguished 1-cells in the map. F = A;B;C;D Y (1 4 5 7 12 14 15) ; ; ; ; ; ; Question 5. Using Karnaugh map, nd a minimal product-of-sums expression for the logic function in Question 4. Indicate the distinguished 0-cells in the map. Using Karnaugh map, nd a minimal sum-of-products expression for the following logic function. Indicate the distinguished 1-cells in the map. F Question 6. = A;B;C;D X (1 5 6 7 9 13) + (4 15) ; ; ; ; ; d ; Question 7. Using Karnaugh map, nd a minimal product-of-sums expression for the logic function in Question 6. Indicate the distinguished 0-cells in the map. Any set of logic-gate types that can realize any logic function is called a complete set of logic gates. For example, 2-input AND gates, 2-input OR gates, and inverters are a complete set, because any logic function can be expressed as a sum of products of variables and their complements, and AND and OR gates with any number of inputs can be made from 2-input gates. Do 2-input NAND gates form a complete set of logic gates? Prove your answer. Question 8. ...
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## This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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