hw3_solution_cs231_sp08_uiuc.html

# hw3_solution_cs231_sp08_uiuc.html -

This preview shows pages 1–4. Sign up to view the full content.

Sheet1 Page 1 <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>CS231 Spring 2008 Homework 3 Solution</title> <link rel="stylesheet" type="text/css" href="/~cs231/style.css" /> <style type="text/css"> ol li { margin-top: 1em </style> </head> <body> <?xml version="1.0" encoding="us-ascii"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <h2 align="center"> CS231 Spring 2008<br> Homework 3 Solution </h2> <hr> <ol> <!-- ========== Problem 1 ========== --> <li> (10pts) Show how to build a 4-to-16 decoder, using <b> only</b> 2-to-4 decoders (no gates). Your decoder should accept four inputs S3-S0, and have sixteen outputs D15-D0.<br> <br> <b>Solution:</b><br> <br> <img border="0" src="1a.png" width="342" height="330"><br> <br> <!-- ========== Problem 2 ========== --> <hr><li> (10pts) Circuit Design: Consider the Boolean function F(x,y,z) = xy + z'(y + x)(z + x')<br> <br> <ol type=a> <li>Simplify this expression to a minimum number of literals using the Boolean identities from lecture. Specify the name or formula of the identity used at each step.<br> <br> <b>Solution:<br> </b><br> = xy + z' ( yz + x'y + xz + xx' )&nbsp

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sheet1 Page 2 by x' * x = 0<br> by Distributive<br> by x' * x = 0<br> by Distributive<br> by (x + x'y) = (x + y)<br> by Distributive <br> <li>Implement the function using a minimum number of AND, OR, and NOT gates.<br> <br> <b>Solution:<br> </b><br> <img border="0" src="2b.png"><br> <li>Implement the function using a minimum number of NAND gates.<br> <br> <b>Solution:<br> </b><br> The minimum number of NAND gates you need is 6. <br> <img border="0" src="2c.png"><br> <li>Implement the function using a 3-to-8 Active-Low decoder and only one multi-input AND gate.<br> <br> <b>Solution:</b><br> <br> <img border="0" src="2d.png"><br> <br></ol> <!-- ========== Problem 3 ========== --> <hr><li> (10 pts) Circuits using Decoders:<br> <ol type =a > <li>Draw a circuit for the following function F using a 3-to-8 decoder (note this is not Active-Low) and one OR gate.<br> <br> <b>Solution:</b><br> <br> <img border="0" src="3a.png"><br> <br> <li>Draw a circuit for the following function G using only one (active-low) 2-to-4 decoder from LogicWorks.<br> Err:510 (<b>Hint</b>: Since there is only one zero in the K-maps, consider under what condition will a certain output pin of 2-4 decoder output zero.)<br>
Sheet1 Page 3 <br> <b>Solution:</b><br> <br> <img border="0" src="3b.png"><br>

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/10/2008 for the course CS 231 taught by Professor - during the Spring '08 term at University of Illinois at Urbana–Champaign.

### Page1 / 28

hw3_solution_cs231_sp08_uiuc.html -

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online