# Boolean Algebra and Duality Principle-Digital Logic Design-Assignment, Exercises for Digital Logic Design and Programming. Punjab Engineering College

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This course includes logic operators, gates, combinational and sequential circuits are studied along with their constituent elements comprising adders, decoders, encoders, multiplexers, as well as latches, flip-flops, co...
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EE Department Labs

EE241 DLD  Page 1

Home Assignment No-2

Subject: Digital Logic Design Marks: 100 Course: BEE-2CD Issue: 29 Feb2012

Due on: 08 Mar 2012 Note: (10:00 AM)

Attempt the given problem set in a sequential order. Show complete work. Write relevant postulates and theorems where required.

Make an index on the front page showing summary of the problems solved along-with page numbers and also specify the missing ones.

No late submissions will be accepted unless a prior approval from the teacher has been obtained with extreme genuine reasons. The assignments submitted after due date/time will be graded zero.

University has zero tolerance for plagiarism and serious penalties apply. All assignments found mutually copied will be marked zero and such recurrence will result award of zero out of total assignment weight age.

All the students will submit a certificate with the assignment work stating the originality of their efforts and no copying from others.

Note that Ten Marks are reserved for neat work, table of contents, and certificate to be attached with the assignment work.

Problem No-1 Demonstrate by means of truth tables the validity of following identities:

a. The second distributive law: X+YZ=(X+Y)(X+Z) b. X΄Y+Y΄Z+XZ΄=XY΄+YZ΄+X΄Z c. (XYZ)΄=X΄+Y΄+Z΄

Problem No-2 Simplify algebraically the following Boolean expressions to the

indicated number of literals/terms: a. W΄X(Z΄+Y΄Z)+X(W+W΄YZ) to one literal

b. (X+W)(YZ)+XW΄ to three terms c. (A+B΄+C+E΄)(A+B΄+D΄+E)(B΄+C΄+D΄+E΄) to five terms Problem No-3 Find the complement of the following expressions by DeMorgan’s  law

and Duality principle: a. g=(w+x΄+y)(w΄+x+z)(w+x+y+z). b. h=(a+b΄c)d΄+(a΄+c΄)(c+d).

Problem No-4 Convert the following expression to sum-of-minterms and product- of-maxterms forms algebraically: F=A+B+A΄B΄C΄D

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EE241 DLD  Page 2

Problem No-5 Convert the following functions to the indicated forms: a. f1=a΄c΄d+a΄cd΄+bc to product-of-sums b. f2=(w+x΄+z)(w΄+y+z΄)(x+y+z) to sum-of-products

Problem No-6 By substituting the Boolean expression equivalent of the binary

operations, show the following: a. NAND is commutative but not associative. b. Inhibition is neither commutative nor associative. c. Exclusive-OR is both commutative as well as associative.

______________________________________________________________________ “Good Luck”

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