Al-Imam Muhammad Ibn Saud Islamic University

College of Computer and Information Sciences

2edsemester, 1435 H / 2014

CS 106

Digital design

CS 106

Sheet #4 Exercises to be submitted are highlighted in red and they are

due on Monday (10-3-2014) 7:30 A.M

Objectives: Understanding how to represent a Boolean function.

Understanding digital logic gates.

Understanding the map method for simplifying Boolean expressions.

Submission policy: Submit all required exercise Cheating is not allowed ,all students will take zero Sunday(almost) is the deadline to submit the home work. Every sheet must be submitted on due date ,if you don't be on time you will lose the

grade. Being absent from a class will not be considered as an excuse. Submit your home work via Blackboard. You have to write your names, ids, sheet # and section # on your sheet cover page. Upload sheet file with cover

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Student namesStudent IDs

Section

Al-Imam Muhammad Ibn Saud Islamic University

College of Computer and Information Sciences

2edsemester, 1435 H / 2014

CS 106

Digital design

Exercise 1: From truth table, simplify the following Boolean functions T1 and T2 to a minimum number of literals:

a)

T1=

T2=

b) Obtain the truth table of the function T1 from the simplified expression and show that it is the same as the original.

c) Draw logic diagrams of the circuits that implement the original and simplified function T1.

Exercise 2: For the Boolean function:

F(x,y,z)= xy+xyz'+xyz+x'z

a) Obtain the truth table of F.

b) Express each function in sum-of-minterms and product-of-maxterms.

Exercise 3: Given that F1(x,y,z)=∑m(0,1,2) and F2(x,y,z)= ∏M(2,3,4,5):

a) Give the representation for F1+F2 as sum of minterms.b) Give the representation for F1+F2 as product of maxterms.c) Give the representation for F1'+F2' as sum of minterms.d) Give the representation for F1'+F2' as product of of maxterms.

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A B C T1 T20 0 0 0 10 0 1 0 10 1 0 1 00 1 1 1 01 0 0 1 01 0 1 1 01 1 0 0 11 1 1 0 1

Al-Imam Muhammad Ibn Saud Islamic University

College of Computer and Information Sciences

2edsemester, 1435 H / 2014

CS 106

Digital design

Exercise 4: Convert the following expression into sum of products and product of sums: (AB + C) (B+C'D)

Exercise 5: Express the following function as a sum of minterms and a product of maxterms: (B'C+AB)

1- Sum of minterms: 2- Proudct of maxterms:

Exercise 6:

1) Consider the below function:

a) What is the corresponding K-Map:

b) Using the K-Map, Simplify to sum-of-products

c) Using the K-Map, Simplify to sum-of-products

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00

01

11

10

00 01 11 10wxyz

Al-Imam Muhammad Ibn Saud Islamic University

College of Computer and Information Sciences

2edsemester, 1435 H / 2014

CS 106

Digital design

2) Consider the below circuit:

a) Give the Boolean expression of output F.b) Simplify the Boolean expression using k-maps.

Exercise 7: Exercises from the text book 5th edition:2.18 + 2.20 (a,b)+ 2.21(a,b) + 2.24 + 2.29

Exercise 8: 1) Exercise 3.1 (text book, 4th edition, page 132) :Simplify the following Boolean functions, using three-variable maps:

a)

b)

2) Exercise 3.3 (text book, 4th edition, page 132) :Simplify the following Boolean expressions, using three-variable maps:

a)

b)

3) Exercise 3.5 (text book, 4th edition, page 132) :Simplify the following Boolean functions, using four-variable maps:

a)

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Al-Imam Muhammad Ibn Saud Islamic University

College of Computer and Information Sciences

2edsemester, 1435 H / 2014

CS 106

Digital design

b)

4) Exercise 3.6 (text book, 4th edition, page 132) :Simplify the following Boolean expressions, using four-variable maps:

a)

b)

5) Exercise 3.8 (text book, 4th edition, page 132) :Find the minterms of the following Boolean expressions by first plotting each function in a map:

a)

b)

6) Exercise 3.9 (text book, 4th edition, page 133) :Find all the prime implicants for the following Boolean functions, and determine which are essential:

a)

b)

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