Digital Logic Design

Karnaugh Maps from Expressions

Simplifying Boolean Expressions

Holiday Detector

Problem 02: Karnaugh Maps from Truth Tables Write fully simplified sum-of-products expressions for the logic functions W, Y, and Z represented by the following truth tables (The 2 entries are "don't care" states). W 1 x 1 Y 1 0 0 Z 0 1 0 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 x 0 1 x 10 1 0 1 1 0 1 Problem 03: Simplifying Boolean Expressions Write fully simplified sum-of-products expressions for following Boolean expressions. (a) W = ACD+AD+BC+CD (b) X = ABCD+ABD+ABC+BCD+ACD (c) Y = ABCD+ABCD+ABCD+ABCD+ABCD+ABCD+ABCD+ABCD+ ABCD (d) Z= (A+B+C) (B+C) + (AB+B) Hint: It may be helpful to obtain the truth table for this expression first. Problem 04: Holiday Detector The Office of Personal Management for the U.S. Federal Government defines ten federal holi- days. The 2020 Holiday Schedule can be found at http://www.opm.gov/policy-data-oversight/snow- dismissal-procedures/federal-holidays/#url=2020, and is reproduced in Table 1. Use four bits, M3, M2, M, and Mo to represent a month, where Jan - 11000012, Feb ~ 210 00102, et cetera to Dec with all other bit patterns never appearing. 1210 11002, (a) Write the truth table for the logic function H which is high when there is a holiday in the month corresponding to the input M3 M2M Mo- (b) Write a maximally simplified expression for H. Date Holiday Wednesday, January 1 New Year's Day Monday, January 20 Birthday of Martin Luther King, Jr. Monday, February 17* Washington's Birthday Monday, May 25 Memorial Day Thursday, July 3** Independence Day Monday, September 7 Labor Day Monday, October 12 Columbus Day Wednesday, November 11 Veterans Day Thursday, November 26 Thanksgiving Day Friday, December 25 Christmas Day * This holiday is designated as "Washington's Birthday" in section 6103(a) of title 5 of the United States Code, which is the law that specifies holidays for Federal employees. Though other institutions such as state and local governments and private businesses may use other names, it is our policy to always refer to holidays by the names designated in the law. ** July 1, 2020 (the legal public holiday for Independence Day), falls on a Saturday. For most Federal employees, Friday, July 3, will be treated as a holiday for pay and leave purposes. Table 1: 2020 Holiday Schedule