Tuesday, 7 October 2014
The basic properties of Boolean algebra are commutative property, associative Property
and distributive property.
2) State the associative property of boolean algebra.
The associative property of Boolean algebra states that the OR ing of several variables
results in the same regardless of the grouping of the variables. The associative property is stated
A+ (B+C) = (A+B) +C
3) State the commutative property of Boolean algebra.
The commutative property states that the order in which the variables are OR ed makes
no difference. The commutative property is:
4) State the distributive property of Boolean algebra.
The distributive property states that AND ing several variables and OR ing the result
With a single variable is equivalent to OR ing the single variable with each of the the several
Variables and then AND ing the sums. The distributive property is:
A+BC= (A+B) (A+C)
5) State the absorption law of Boolean algebra.
The absorption law of Boolean algebra is given by X+XY=X, X(X+Y) =X.
6) State De Morgan's theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They
1) The complement of a product is equal to the sum of the complements.
(AB)' = A' + B'
2) The complement of a sum term is equal to the product of the complements.
(A + B)' = A'B'
7) Reduce A (A + B)
A (A + B) = AA + AB
= A (1 + B) [1 + B = 1]
8) Reduce A'B'C' + A'BC' + A'BC
A'B'C' + A'BC' + A'BC = A'C'(B' + B) + A'B'C
= A'C' + A'BC [A + A' = 1]
= A'(C' + BC)
= A'(C' + B) [A + A'B = A + B]
9) Reduce AB + (AC)' + AB’C (AB + C)
AB + (AC)' + AB’C (AB + C) = AB + (AC)' + AAB'BC + AB'CC
= AB + (AC)' + AB'CC [A.A' = 0]
= AB + (AC)' + AB'C [A.A = 1]
= AB + A' + C' =AB'C [(AB)' = A' + B']
= A' + B + C' + AB'C [A + AB' = A + B]
= A' + B'C + B + C' [A + A'B = A + B]
= A' + B + C' + B'C
=A' + B + C' + B'
=A' + C' + 1
= 1 [A + 1 =1]
10) Simplify the following expression Y = (A + B) (A + C’) (B' + C’)
Y = (A + B) (A + C’) (B' + C’)
= (AA' + AC +A'B +BC) (B' + C') [A.A' = 0]
= (AC + A'B + BC) (B' + C’)
= AB'C + ACC' + A'BB' + A'BC' + BB'C + BCC'
= AB'C + A'BC'
11) Show that (X + Y' + XY) (X + Y') (X'Y) = 0
(X + Y' + XY)(X + Y')(X'Y) = (X + Y' + X) (X + Y’) (X' + Y) [A + A'B = A + B]
= (X + Y’) (X + Y’) (X'Y) [A + A = 1]
= (X + Y’) (X'Y) [A.A = 1]
= X.X' + Y'.X'.Y
= 0 [A.A' = 0]
12) Prove that ABC + ABC' + AB'C + A'BC = AB + AC + BC
ABC + ABC' + AB'C + A'BC=AB(C + C') + AB'C + A'BC
=AB + AB'C + A'BC
=A(B + B'C) + A'BC
=A(B + C) + A'BC
=AB + AC + A'BC
=B(A + C) + AC
=AB + BC + AC
=AB + AC +BC ...Proved
13) Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC (B + B’) + AB (C + C’) + (A + A') BC
=ABC + ABC' + AB'C + AB'C' + ABC + ABC' + ABC
=ABC + ABC' +AB'C + AB'C' [A + A =1]
14) Define duality property.
Duality property states that every algebraic expression deducible from the postulates Of
Boolean algebra remains valid if the operators and identity elements are interchanged. If
the dual of an algebraic expression is desired, we simply interchange OR and AND operators and
replace 1's by 0's and 0's by 1's.
15) Find the complement of the functions F1 = x'yz' + x'y'z and F2 = x (y'z' + yz).
By applying De-Morgan's theorem.
F1' = (x'yz' + x'y'z)' = (x'yz')'(x'y'z)' = (x + y' + z)(x + y +z')
F2' = [x (y'z' + yz)]' = x' + (y'z' + yz)'
= x' + (y'z')'(yz)'
= x' + (y + z) (y' + z')
16) Simplify the following expression
Y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C
Monday, 10 February 2014
- Write short notes on :Protocol Architecture.
- Discuss TCP / IP protocol layer architecture and functions in detail.(**)
- Write short note on (c) Line Configuration.-5
- List and explain transmission impairments.
- Write short notes on any two of the following:
- Compare the three basic modulation techniques for transforming digital data into analog signals. (5)
- What is pulse stuffing? Explain how it is helpful in design of TEDM. (5)
- (b) Explain the concept of Delta Modulation.***
- (a) Draw the wave forms and explain the following coding schemes:
- Explain Data Communications Interfacing with neat diagrams.
- Explain about Amplitude modulation and Angle modulation. 10
- Differentiate between Amplitude shift keying, frequency shift keying and phase shift keying. (4)