SUBJECT NAME : DIGITAL SYSTEMS DESIGN
SUBJECT CODE : EC3352
IMPORTANT QUESTIONS
PART – A
UNIT - I
DIGITAL FUNDAMENTALS
1. State Demorgan’s Theorem.
De Morgan suggested two theorems that form important part of Boolean
algebra. They are,
i. The complement of a product is equal to the sum of the complements.
(AB)' = A' + B'
ii. The complement of a sum term is equal to the product of the complements.
(A + B)' = A'B'
2. Implement using NAND gates only, F = x y z + x′ y′.
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,3. What are Don’t care terms?
In some logic circuits certain input conditions never occur, therefore the
corresponding output never appears. In such cases the output level is not defined, it
can be either high or low. These output levels are indicated by ‘X’ or ‘d’ in the truth
tables and are called don’t care conditions or incompletely specified functions.
4. Apply De-Morgan’s theorem to [ (A+B) + C ] ′.
Given [(A+B)+C] ′ = (A+B) ′.C′
= (A′.B′).C′
[(A+B)+C] ′ = A′B′C′
5. Convert 0.35 to equivalent hexadecimal number.
Given (0.35)10 =0.35 x 16=5.60
=0.60 x 16=9.60
=0.60 x 16=9.60
(0.35)10 = (0.599)16
6. Convert Y=A+BC′+AB+A′BC into canonical form.
Given Y=A+BC′+AB+A′BC
Y=A(B+B′)(C+C′)+(A+A′)BC′+AB(C+C′)+A′BC
Y=ABC+ABC′+AB′C+AB′C′+ABC′+A′BC′+ABC+ABC′+A′BC
Y=ABC+ABC′+AB′C+AB′C′+A′BC′+A′BC
7. Define ‘min term’ and ‘max term’.
A product term containing all the variables of the function in either complemented or
uncomplemented form is called a min term.
A sum term containing all the variables of the function in either complemented or
uncomplemented form is called a max term.
8. Prove that the logical sum of all min terms of a Boolean function of 2 variables is 1.
Consider two variables as A and B. For two variables A and B minterms are:
A′B′,A′B,AB′,AB. The logical sum of these minterms are given by
F= A′B′+A′B+AB′+AB
= A′(B′+B)+A(B′+B) (B′+B=1)
= A′(1)+A(1) (A′+A=1)
F=1
Hence it is to be proved.
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, 9. Show that a positive logic NAND gate is a negative logic NOR gate.
Truth table for positive logic NAND gate and negative logic NOR gates are same and
hence a positive logic NAND gate is negative logic NOR gate.
10. Simplify the following Boolean Expression to a minimum number of literals.
(BC′+A′D)(AB′+CD′)
F=(BC′+A′D)(AB′+CD′)
=BC′AB′+BC′CD′+A′DAB′+A′DCD′ (A.A′=0)
= AB B′C′+BCC′D′+AA′ B′D+A′CDD′
F=0
11. Simplify the given Boolean Expression F=x′+xy+xz′+xy′z′.
F=x′+xy+xz′+xy′z′
= x′+x(y+z′+y′z′) (A+A′B=A+B)
= x′+y+z′+y′z′
= x′+y+z′(1+y′) (1+A′=1)
F = x′+y+z′
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SUBJECT CODE : EC3352
IMPORTANT QUESTIONS
PART – A
UNIT - I
DIGITAL FUNDAMENTALS
1. State Demorgan’s Theorem.
De Morgan suggested two theorems that form important part of Boolean
algebra. They are,
i. The complement of a product is equal to the sum of the complements.
(AB)' = A' + B'
ii. The complement of a sum term is equal to the product of the complements.
(A + B)' = A'B'
2. Implement using NAND gates only, F = x y z + x′ y′.
For More Visit : www.LearnEngineering.in
,3. What are Don’t care terms?
In some logic circuits certain input conditions never occur, therefore the
corresponding output never appears. In such cases the output level is not defined, it
can be either high or low. These output levels are indicated by ‘X’ or ‘d’ in the truth
tables and are called don’t care conditions or incompletely specified functions.
4. Apply De-Morgan’s theorem to [ (A+B) + C ] ′.
Given [(A+B)+C] ′ = (A+B) ′.C′
= (A′.B′).C′
[(A+B)+C] ′ = A′B′C′
5. Convert 0.35 to equivalent hexadecimal number.
Given (0.35)10 =0.35 x 16=5.60
=0.60 x 16=9.60
=0.60 x 16=9.60
(0.35)10 = (0.599)16
6. Convert Y=A+BC′+AB+A′BC into canonical form.
Given Y=A+BC′+AB+A′BC
Y=A(B+B′)(C+C′)+(A+A′)BC′+AB(C+C′)+A′BC
Y=ABC+ABC′+AB′C+AB′C′+ABC′+A′BC′+ABC+ABC′+A′BC
Y=ABC+ABC′+AB′C+AB′C′+A′BC′+A′BC
7. Define ‘min term’ and ‘max term’.
A product term containing all the variables of the function in either complemented or
uncomplemented form is called a min term.
A sum term containing all the variables of the function in either complemented or
uncomplemented form is called a max term.
8. Prove that the logical sum of all min terms of a Boolean function of 2 variables is 1.
Consider two variables as A and B. For two variables A and B minterms are:
A′B′,A′B,AB′,AB. The logical sum of these minterms are given by
F= A′B′+A′B+AB′+AB
= A′(B′+B)+A(B′+B) (B′+B=1)
= A′(1)+A(1) (A′+A=1)
F=1
Hence it is to be proved.
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, 9. Show that a positive logic NAND gate is a negative logic NOR gate.
Truth table for positive logic NAND gate and negative logic NOR gates are same and
hence a positive logic NAND gate is negative logic NOR gate.
10. Simplify the following Boolean Expression to a minimum number of literals.
(BC′+A′D)(AB′+CD′)
F=(BC′+A′D)(AB′+CD′)
=BC′AB′+BC′CD′+A′DAB′+A′DCD′ (A.A′=0)
= AB B′C′+BCC′D′+AA′ B′D+A′CDD′
F=0
11. Simplify the given Boolean Expression F=x′+xy+xz′+xy′z′.
F=x′+xy+xz′+xy′z′
= x′+x(y+z′+y′z′) (A+A′B=A+B)
= x′+y+z′+y′z′
= x′+y+z′(1+y′) (1+A′=1)
F = x′+y+z′
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