ECE252 homework 3

ECE252 homework 3 - CS/ECE 252 Introduction to Computer...

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CS/ECE 252 Introduction to Computer Engineering Spring 2008 All Sections Instructor  David A. Wood Homework 3 Problem 1 Draw a logic circuit corresponding to the following logic expression. Your circuit must use only 2-input AND, 2-input OR, and NOT gates. Z = ((A OR B) AND (NOT (C AND D))) OR (NOT (A) AND (E OR F)) Problem 2 Consider a logic circuit which has four inputs A, B, C and D and an output Z. The output Z is 1 if and only if the total number of 1s among A, B, C and D is strictly greater than 2 (not equal). a. Draw a truth table for a logic circuit that performs this function.

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A B C D 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 Z 0 0 0 0 0 0 0 1
b. Write the logic expression corresponding to the circuit. A simple way to derive the logic expression from every truth table is to follow the method presented in Problem 5: 1. Locate the lines in the truth table where the output becomes 1. 2. For each of these lines, find the circuit of AND and NOT gates that gives an output of 1. 3. Connect those outputs as inputs in a big OR gate. Applying this method to the truth table above gives us: o For ABCD=0111, the expression (A AND B AND C AND D) is true. o For ABCD=1011, the expression (A AND B AND C AND D) is true. o

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This note was uploaded on 03/27/2008 for the course CS 252 taught by Professor Wood during the Spring '08 term at University of Wisconsin.

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ECE252 homework 3 - CS/ECE 252 Introduction to Computer...

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