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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)(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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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.

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“**Good Luck”
**

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