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

## Digital Logic Design

Description: 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, counters and registers. This assignment includes: Boolean, Algebra, Duality, Principle, Truth, Tables, Identities, Distributive, Law, Minterms, Maxterms
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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.
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)(YZ)+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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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.
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Good Luck
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