Homework_4 - BME 303 Copyright © Orly Alter 2009 Last...

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Unformatted text preview: BME 303 Copyright © Orly Alter 2009 Last Name: Homework 4 Due on Oct 13, 2009 First Name: Lab Session: 143__ Homework Instructions: 1. Each HW must be stapled [50% score deducted otherwise]. 2. Use this page as a cover. 3. Show details of your work, and explain in words, except in the most obvious cases. 4. Your work must be neat and clear. 5. Each section is 10%, unless it is specified differently, for a total of 160%. Maitland and Thayer’s Binary Adder United States Patent 4,052,604 Industrial Logic Structures Design with: a. Truth Tables, b. Boolean Algebra, c. Venn Diagrams, d. Karnaugh Maps, and e. Schematic Logic Circuits. 1 BME 303 Copyright © Orly Alter 2009 Homework 4 Due on Oct 13, 2009 Read the invention “Binary Adder,” by Maitland and Thayer (United States Patent 4,052,604, 1977); a reprint is available at the course website – http://www.bme.utexas.edu/research/orly/teaching/BME303/Maitl and_Thayer.pdf a. Write the truth table that corresponds to the “service logic” structure that is drawn in Fig. 2 of the patent. Input Ai Output ANDi Bi XORi NORi b. Complete below the Venn diagrams for ANDi, XORi and NORi. Do these overlap? What is their intersection? (30%) A B ANDi A B XORi A B NORi c. Evaluate, based on the truth table of Question 5(a), the intersection of ANDi, XORi and NORi, that is, evaluate: (ANDi) AND (XORi) AND (NORi) 2 BME 303 Copyright © Orly Alter 2009 Homework 4 Due on Oct 13, 2009 d. Is your answer to Question 5(c) consistent with your answer to Question 5(b)? Explain. e. Expand the truth table of Question 5(a) below so that it can be compared to that of the full-adder of Question 4(a) (20%). Input A 0 0 0 0 1 1 1 1 Service Logic Output Adder Output ANDi XORi NORi Si Ci=Cout Bi 0 0 1 1 0 0 1 1 Ci-1=Cin 0 1 0 1 0 1 0 1 f. Use the expanded truth table to prove Equations (1–6) in Column 2 of the patent (20%). Explain each proof in words. g. Convert the truth table of Question 5(e) to logic equations for the adder’s outputs Si and Ci=Cout in terms of the service logic outputs ANDi=(Ai AND Bi), XORi=(Ai XOR Bi) and NORi=(Ai NOR Bi) and the input carry Ci-1 (20%). h. Based on your logic equations, draw the schematics for the logic structure that would take as its inputs the service logic outputs ANDi=(Ai AND Bi), XORi=(Ai XOR Bi) and NORi=(Ai NOR Bi) and the input carry Ci-1 and would deliver as its outputs the adder’s outputs Si and Ci=Cout (20%). i. Compare the schematics of the Maitland and Thayer’s binary adder to these of the full-adder of Question 4. What are the advantages of this adder over the full-adder of Question 4 (20%)? 3 ...
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This note was uploaded on 01/12/2010 for the course BME 14345 taught by Professor Orlyalter during the Fall '09 term at University of Texas at Austin.

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