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Digital Logic - Logic functions & Minimization

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1:   Which of the following respectively represent commutative law, Associative law and Distributive law ?
I. A.(B C)=(A.B).C
II. A.(B+C)=A.B+A.C
III. A + B = B + A
CODES
A. I,III, and II
B. II, I and III
C. III, II and I
D. III, I and II
 
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Option: D

Explanation :

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2:  

The number of canonical expressions that can be developed over a 3-valued boolean algebra is

A.

8
B.

16
C.

32
D.

256
 
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Option: D

Explanation :

Canonical form=SOP or POS
No of min/MAX terms=23=8. 
Therefore, Canonical form will have 28 have  terms.
Zero term canonical forms=8C0=1. 
One term canonical forms=8C1=8. 
Two term canonical forms=8C2=28 
Similarly total number of canonical expressions=
8C0+8C1+8C2+8C3+8C4+8C5+8C6+8C7+8C8=256

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Gagan Kumar said: (11:49pm on Sunday 12th November 2017)
(X Y(1 X))(X Z)(X Y)(X Z)X=YZ

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3:  

Simplified form of the boolean expression (X + Y + XY) (X + Z) is

A.

X + Y + Z
B.

XY + YZ
C.

X + YZ
D.

XZ + Y
 
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Option: C

Explanation :

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priya said: (9:40pm on Thursday 5th September 2013)
xx xy xxy xz zy zxyx xy xz zy zxyx zy zxyx zy(x 1=1)
Gagan Kumar said: (11:50pm on Sunday 12th November 2017)
(X Y(1 X))(X Z)(X Y)(X Z)(X YZ)

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4:  

Which of the following boolean expressions is not logically equivalent to all of the rest ?

A. ab + (cd)' + cd + bd'
B. a (b + c) + cd
C. ab + ac + (cd)'
D. bd' + c'd' + ab + cd
 
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Option: A

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5:  

A switching function is symmetric with respect to a set of literals if and only if the function remains unchanged after

A. Two of these literals are interchanged
B. Any permutation of the literals
C. All the literals are changed in anticlockwise order
D. All the literals are changed in clockwise order
 
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Option: B

Explanation :

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Syllabus covered in this section is-

  • Logic functions, Minimization,
  • Design and synthesis of combinational and sequential circuits
  • Number representation and computer arithmetic (fixed and floating point)
  • Propositional (Boolean) Logic
  • Satisfiability and Tautology
  • Logic Families: TTL, ECL and C-MOS gates.
  • Boolean algebra and Minimization of Boolean functions
  • Flip-flops-types, race condition and comparison.
  • Design of combinational and sequential Circuits
  • Representation of Integers: Octal, Hex. Decimal and Binary.
  •  2's complement and 1 's complement arithmetic
  • Floating point representation.

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