# UGC NET

This post consists more than 45 questions from COMPUTER ARITHMETIC from previous years UGC NET papers. this will help you to understand the pattern of questions comes under this section. Generally 5 out 50 questions comes from COMPUTER ARITHMETIC. New syllabus issued by the NTA is given in this post. This post also highlight the questions from each years. Try to solve the questions.

Best of luck for your NTA UGC NET preparation.

### COMPUTER ARITHMETIC UGC NET SYLLABUS AND MCQs FROM OLD PAPERS

Computer Arithmetic :

Propositional ( Boolean ) Logic,

Predicate Logic,

Well – formed – formulae ( WFF ),

Satisfiability and

Tautology.

Logic Families :

TTL,

ECL and

CMOS 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.

### DEC 2015

Q1. Which of the following arguments are not valid ?

(a) ” If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”.

(b) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”.

(c) If n is a real number such that n>1, then N2>1. Suppose that N2>1, then n>l.

Codes :

(1) (a)and(c) (2) (b) and (c) (3) (a), (b) and (c) (4) (a) and (b)

Q2. Let P(m, n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.

(a) ∃m∀nP(m,n) (b) ∀n P(1, n) (c) ∀m ∀n P(m, n)

Codes :

(1) (a) – True; (b) – True; (c) – False (2) (a) – True; (b) – False; (c) – False

(3) (a) – False; (b) – False; (c) – False (4) (a) – True; (b) – True; (c) – True

Q3. Match the following terms:

List-I List-II

(a) Vacuous proof (i) A proof that the implication p → q is true based on the fact that p is false.

(b) Trivial proof (ii) A proof that the implication p → q is true based on the fact that q is true.

(c) Direct proof (iii) A proof that the implication p → q is true that proceeds by showing that q must be true when p is true.

(d) Indirect proof (iv) A proof that the implication p → q is true that proceeds by showing that p must be false when q is false.

Codes :

(a) (b) (c) (d)

(1) (i) (ii) (iii) (iv)

(2) (ii) (iii) (i) (iv)

(3) (iii) (ii) (iv) (i)

(4) (iv) (iii) (ii) (i)

Q4. Consider the compound propositions given below as :

(a) p∨~(p∧q) (b) (p∧~q)∨~(p∧q) (c) p∧(q∨r)

Which of the above propositions are tautologies ?

(1) (a) and (c) (2) (b) and (c) (3) (a) and (b) (4) (a), (b) and (c)

Q5. Which of the following property/ies a Group G must hold, in order to be an Abelian group ?

(a) The distributive property

(b) The commutative property

(c) The symmetric property Codes :

(1) (a) and (b) (2) (b) and (c) (3) (a) only (4) (b) only

JUNE 2015

Q6. Consider the following statements :

(a) Boolean expressions and logic networks correspond to labelled acyclic digraphs.

(b) Optimal boolean expressions may not correspond to simplest networks.

(c) Choosing essential blocks first in a Karnaugh map and then greedily choosing the largest remaining blocks to cover may not give an optimal expression.

Which of these statement(s) is/are correct ?

(1) (a) only

(2) (b) only

(3) (a)and(b)

(4) (a), (b) and (c)

Q7. Consider a full – adder with the following input values :

(a) x = l, y = 0 and Ci (carry input) = 0

(b) x = 0,y = l and Ci = l

Compute the values of S(sum) and Co(carry output) for the above input values.

(1) S = l, Co =0 and S= 0, Co=l (2) S = 0,Co =0 and S= l, Co =1

(3) S = l, Co = l and S= 0, Co= 0 (4) S = 0,Co = l and S= l, Co = 0 ¬¬¬

Q8. “If my computations are correct and I pay the electric bill, then I will run out of money. If I don’t pay the electric bill, the power will be turned off. Therefore, if I don’t run out of money and the power is still on, then my computations are incorrect.”

Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where ¬ means NOT)

(1) if (c∧b)→r and ¬b→¬p, then (¬r∧p)→¬c

(2) if (c∨b)→r and ¬b→¬p, then (r∧P)→c

(3) if (c∧b)→r and ¬p→¬b, then (¬r∨p)→¬c

(4) if (c∨b)→r and ¬b→¬p, then (¬r∧p)→¬c

Q9.Match the following :

List-I List – II

(a) (p→q)⇔(¬q→¬p) (i) Contrapositive

(b) [(p∧q)→r]⇔[p→(q→r)] (ii) Exportation law

(C) (p→q)⇔[(p∧¬q)→o] (iii) Reductio ad absurdum

(d) (p↔q)⇔[(p→q)∧(q→p) (iv) Equivalence

Codes :

(a) (b) (c) (d)

(1) (i) (ii) (iii) (iv)

(2) (ii) (iii) (i) (iv)

(3) (iii) (ii) (iv) (i)

(4) (iv) (ii) (iii) (i)

Q10. Consider a proposition given as:

” x≥ 6, if x2≥ 25 and its proof as:

If x≥6, then x2 = x.x≥6-6 = 36≥25

Which of the following is correct w.r.to the given proposition and its proof ?

(a) The proof shows the converse of what is to be proved.

(b) The proof starts by assuming what is to be shown.

(c) The proof is correct and there is nothing wrong.

(1) (a) only

(2) (c) only

DEC 2014

Q11. The BCD adder to add two decimal digits needs minimum of

(A) 6 full adders and 2 half adders

(B) 5 full adders and 3 half adders

(C) 4 full adders and 3 half adders

(D) 5 full adders and 2 half adders

Q12. The Excess-3 decimal code is a self-complementing code because

(A) The binary sum of a code and its 9’s complement is equal to 9.

(B) It is a weighted code.

(C) Complement can be generated by inverting each bit pattern.

(D) The binary sum of a code and its 10’s complement is equal to

JUNE 2014

Q13. How many different truth tables of the compound propositions are there that involve the propositions p & q ?

(A) 2 (B) 4 (C) 8 (D) 16

Q14. A Boolean function F is called self- dual if and only if

F(X1, X2, … .Xn) = F(X1‘, X2‘,……Xn‘)

How many Boolean functions of degree n are self-dual ?

(A) 2n (B) (2)2n (C) (2)n2 (D) (2)2n-1

Q15. Which of the following statement(s) is (are) not correct ?

i. The 2′ s complement of 0 is 0.

ii. In 2’s complement, the left most bit cannot be used to express a quantity.

iii. For an n-bit word (2’s complement) which includes the sign bit, there are 2n-1 positive integers, 2n+1 negative integers and one 0 for a total of 2n unique states.

iv. In 2’s complement the significant information is contained in the 1’s of positive numbers and 0’s of the negative numbers.

(A) i & iv (B) i & ii (C) iii (D) iv

Q16. The notation ∃!xP(x) denotes the proposition “there exists a unique x such that P(x) is true”.

Give the truth values of the following statements :

I. ∃!xP(x) → ∃xP(x)

II. ∃!x ¬P(x) → ¬∀xP(x)

(A) Both I & II are true.

(B) Both I & II are false.

(C) I – false, II – true

(D) I – true, II – false

Q17. Give a compound proposition involving propositions p, q and r that is true when exactly two of p, q and r are true and is false otherwise.

(A) (p∨q∧¬ r) ∧ (p∧¬q∧ r) ∧ (¬p∧q∧ r)

(B) (p∧q∧¬ r) ∧ (p∨q∧¬ r) ∧ (¬p∧q∧ r)

(C) (p∧q∧¬ r) ∨ (p∧¬q∧ r) ∧ (¬p∧q∧ r)

(D) (p∧q∧¬ r) ∨ (p∧¬q∧ r) ∨ (¬p∧q∧ r)

DEC 2013

Q18. The dual of a Boolean expression is obtained by interchanging

(A) Boolean sums and Boolean products

(B) Boolean sums and Boolean products or interchanging 0’s and 1 ‘s

(C) Boolean sums and Boolean products and interchanging 0’s & 1’s

(D) Interchanging 0’s and 1’s

Q19. Given that (292) 10 = (1204)^ in some number system x. The base x of that number system is

(A) 2

(B) 8

(C) 10

(D) None of the above

Q20. The sum of products expansion for the function

F(x, y, z) = (x + y)z is given as

(A) xyz + xyz + xyz

(B) xyz + xyz + xyz

(C) xyz + xyz + xyz

(D) xyz + xyz + xyz

Q21. Let P(m, n) be the statement

“m divides n” where the universe of discourse for both the variables is the set of positive integers. Determine the truth values of each of the following propositions:

I: VmVnP(m,n),

II. 3m Vn P(m, n)

(A) Both I and II are true

(B) Both I and II are false

(C) I – false & II – true

(D) I – true & II – false

**JUNE 2013**

Q22.. Which of the following shall be a compound proposition involving the propositions p, q and r. that is true when exactly two of the p. q and rare true and is false otherwise?

(A) (p∨q∧˥r) ∨ (p∨q∧r) ∧ (˥p∧q∨r)

(B) (p∧q∨r) ∧ (p∧q∧r) ∨ (˥q∨˥p∧˥r)

(C) (p∧q∧˥r) ∨ (p∨˥q∧r) ∨ (˥p∧q∧r)

(D) (p∨r∧q) ∨ (p∧q∧r) ∨ (˥p∧q∧r)

Q23.. The truth value of the statements:

∃!xP(x) → ∃xP(x) and ∃!x˥P(x) → ˥∀xP(x), (where the notation ∃!xP(x) denotes the proposition “There exists a unique x such that P(x) is true”) are :

(A) True and False

(B) False and True

(C) False and False

(D) True and True

Q24. How many different Boolean functions of degree 4 are there?

(A) 2 power 4

(B) 2 power 8

(C) 2 power 12

(D) 2 power 16

Q25. A Boolean operator Ө is defined as follows:

1 Ө 1 =1, 1 Ө 0 = 0, 0 Ө 1= 0 and 0 Ө 0 =1

What will be the truth value of the expression (x Ө y) Ө z = x Ө (y Ө z)?

(A) Always false

(B) Always true

(C) Sometimes true

(D) True when x,y,z are all true

Q26. Which one of the following is decimal value of a signed binary number 1101010, if it is in 2’s complement form ?

(A) -42

(B) – 22

(C) – 21

(D) -106

DEC 2012

Q27. Match the following IC families with their basic circuits :

a. TTL 1. NAND

b. ECL 2. NOR

c. CMOS 3. Inverter Code

a b c

(A) 1 2 3

(B) 3 2 1

(C) 2 3 1

(D) 2 1 3

Q28. Match the following :

a. TTL 1. High fan out

b. ECL 2. Low propagation delay

c. CMOS 3. High power dissipation Code:

a b c

(A) 3 2 1

(B) 1 2 3

(C) 1 3 2

(D) 3 1 2

Q29. Identify the operation which is commutative but not associative ?

(A) OR

(B) NOR

(C) EX-OR

(D) NAND

Note: Both NOR and NAND gates are commutative and not associative

JUNE 2012

Q30. Which of the following logic families is well suited for high-speed operations ?

(A) TTL

(B) ECL

(C) MOS

(D) CMOS

**DEC 2011**

Q31. The proposition ~ qvp is equivalent to

(A) p ->q

(B) q – >p

(C) p <->q

(D) p v q

**JUNE 2011**

Q32. The proposition ~ pÚ q is equivalent to

(A) p ® q

(B) q ® p

(C) p « q

(D) p Ú q

Q33. The absorption law in Boolean algebra say that

(A) X + X = X

(B) X . X = X

(C) x + x . y = x

(D) None of the above

Q34. The number of 1’s present in the binary representation of

10 × 256 + 5 × 16 + 5 is

(A) 5 (B) 6 (C) 7 (D) 8

Q35. The hexadecimal number equivalent to (1762.46)8is

(A) 3F2.89 (B) 3F2.98 (C) 2F3.89 (D) 2F3.98

Q36. (A + B)AB is equivalent to

(A) A ⊕ B

(B) A☉B

(C) (A ⊕ B)☉A

(D) (A☉B) ⊕ A

Q37. A latch is constructed using two cross-coupled

(A) AND and OR gates

(B) AND gates

(C) NAND and NOR gates

(D) NAND gates

Q38. A multiplexer is a logic circuit that

(A) accepts one input and gives several output

(B) accepts many inputs and gives many output

(C) accepts many inputs and gives one output

(D) accepts one input and gives one output

Q39. 8-bit 1’s complement form of –77.25 is

(A) 01001101.0100

(B) 01001101 .0010

(C) 10110010.1011

(D) 10110010.1101

**DEC 2010**

Q40. The decimal number equivalent of (4057.06)8 is

(A) 2095.75

(B) 2095.075

(C) 2095.937

(D) 2095.0937

Q41. AB +(A+ B) is equivalent to

(A) A ⊕ B

(B) A☉B

(C) (A⊕B)☉A

(D) (A☉B)⊕A

Q42. An astable multivibrator has

(A) one stable state

(B) two stable states

(C) no stable states

(D) none of these

Q43. 12-bit 2’s complement of –73.75 is

(A) 01001001.1100

(B) 11001001.1100

(C) 10110110.0100

(D) 10110110.1100

**JUNE 2010**

Q44. Advantage of synchronous sequential circuits over asynchronous ones is

(A) faster operation

(B) ease of avoiding problems due to hazard

(C) lower hardware requirement

(D) better noise immunity

Q45. What is the transitive voltage for the voltage input of a CMOS operating from 10V supply ?

(A) 1V (B) 2V (C) 5V (D) 10 V

Q46. What is decimal equivalent of BCD 11011.1100 ?

(A) 22.0 (B) 22.2 (C) 20.2 (D) 21.2

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