\documentclass[12pt,ifthen]{article} \usepackage{amsmath} \usepackage{amssymb} %\usepackage{html} \usepackage{hyperref} \newcommand{\N}{{\sf N}} \newcommand{\Z}{{\sf Z}} \newcommand{\R}{{\sf R}} \newcommand{\into}{{\rightarrow}} \newcommand{\ceil}[1]{\lceil #1 \rceil} \usepackage{amsthm} \newtheorem{theorem}{Theorem} \begin{document} \centerline{\bf Honors Homework 2} \centerline{Morally Due Mon Feb 14 at 9:00 AM. Dead Cat Feb 16 at 9:00 Am} COURSE WEBSITE: \url{http://www.cs.umd.edu/~gasarch/COURSES/752/S22/index.html} (The symbol before gasarch is a tilde.) \begin{enumerate} \item (20 points) Consider the following table \begin{center} \begin{tabular}{c|c|c|c} X & Y & Z & Output \\ \hline 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \\ \end{tabular} \end{center} \begin{enumerate} \item (10 points) Draw the k-map for the table. \item (10 points) Give the simplified expression from the k-map. \end{enumerate} \item (30 points) Consider the following table \begin{center} \begin{tabular}{c|c|c|c} X & Y & Z & Output \\ \hline 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1\\ 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ \end{tabular} \end{center} \begin{enumerate} \item (10 points) Draw the k-map for the table. \item (10 points) Give the simplified expression from the k-map. \item (10 points) Give the expression in terms of exclusive-or. \end{enumerate} \item (20 points) Consider the following table \begin{center} \begin{tabular}{c|c|c|c|c} W & X & Y & Z & Output \\ \hline 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 \\ 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \\ \end{tabular} \end{center} \begin{enumerate} \item (10 points) Draw the k-map for the table. \item (10 points) Give the simplified expression from the k-map. \end{enumerate} \item (10 points) In recitation, the SR Latch was made up of two NOR Gates. Draw an SR Latch with NAND and NOT gates. \item (10 points) When D = 1 and the clock = 0 what does the clocked D latch produce? \item (10 points) How many AND gates are in a 16-bit register made up of flip-flops? \end{enumerate} \end{document}