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Date: Mon, 02 Dec 1996 15:11:05 GMTServer: NCSA/1.4.2Content-type: text/html<html><head><title>CSE567 Homework Assignment #1</title></head><body bgcolor="#dddddd" text="#000000" link="#0000ee" vlink="501080" alink="ff0000"><h1>CSE 567: Principles of Digital Systems Design </h1><h3>Carl Ebeling, Fall 1996 </h2><hr><h3>Homework 1</h3><p><b>Distributed: Monday Oct. 7 - Due Friday Oct. 11, in class</b><hr><p><ol><li> Prove the following simplification theorems using only axioms andtheorems T1-6 and T9-10 from the notes:<pre>a. (A+B)(A+B') = Ab. (A+B)(A'+B) = AB+A'B</pre><li> Use DeMorgan's law to complement:<pre>ABC+B(C'+D')</pre><li> Simplify the following using the theorems of Boolean algebra:<pre>f(X,Y,Z) = (X+Y)(X'+Y+Z)(X'+Y+Z')</pre><li> Rewrite the following in Product of Sums form, not necessarilyminimized:<pre>f(A,B,C,D) = AB + CD + AC' + A'D</pre><li> Implement the logic function <pre>f(A,B,C,D,E) = ABCDE </pre>using 2-input NAND gates only. Try to minimize worst-case delay.What is the worst-case delay of your circuit assuming each NAND gatehas a delay of 2 ns?<p><li> Find a three-variable function that is its own dual. (Thishighlights the fact that duality and complementation are verydifferent.)<p><li> A 2-bit comparator compares two 2-bit numbers A and B andgenerates two results, A>B and A=B.<br>a. Implement a 2-bit comparator.<br>b. Use the 2-bit comparator that you designed in part (a) to constructat 4-bit comparator.<br>c. Extend the method you used for part (b) to describe how toimplement an n-bit comparator for arbitrary n. Assuming that eachlogic gate has a delay of 1 (unit-delay model), what is the delay ofyour n-bit comparator as a function of n?d. (Extra credit) If your answer for part (c) was not O(logn) thenfind a solution that is.<p><li> Consider a three-out-of-five majority gate called M5, whoseoutput is 1 if at least three of its five inputs are 1.<br>a. Show how to implement a 2-input AND gate using M5 with the inputsconnected appropriately.<br>b. Show how to impement a 3-input OR gate using M5.<br>c. Can you use M5 to implement an inverter?</ol></body><address><hr>ebeling@cs.washington.edu</address><p></html>⌨️ 快捷键说明
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