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Test: Floating Point Number- 2 - Computer Science Engineering (CSE) MCQ


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12 Questions MCQ Test GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Test: Floating Point Number- 2

Test: Floating Point Number- 2 for Computer Science Engineering (CSE) 2024 is part of GATE Computer Science Engineering(CSE) 2025 Mock Test Series preparation. The Test: Floating Point Number- 2 questions and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus.The Test: Floating Point Number- 2 MCQs are made for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Floating Point Number- 2 below.
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Test: Floating Point Number- 2 - Question 1

For interval arithmetic best rounding technique use is ________.

Detailed Solution for Test: Floating Point Number- 2 - Question 1

Rounding to plus and minus infinity are useful in implementing a technique known as interval arithmetic. Interval arithmetic provides an efficient method for monitoring and controlling errors in floating point computations by producing two values for each result. The two values correspond to the lower and upper endpoints of an interval that contains the true result. The width of the interval, which is the difference between the upper and lower endpoints, indicates the accuracy of the result of the endpoints of an interval are not representable then the interval endpoints are rounded down and up respectively.

Test: Floating Point Number- 2 - Question 2

When multiplicand Y is multiplied by multiplier X = xn-1xn-2 ... x0 using bit- pair recording in Booth’s algorithm, partial products are generated according to the following table:

Q. The partial products for rows 5 and 8 are 

Detailed Solution for Test: Floating Point Number- 2 - Question 2


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Test: Floating Point Number- 2 - Question 3

Consider the following floating point format:

Mantissa is a pure fraction is sign-magnitude form.

Q. The decimal number 0.239 x 213 has the following hexadecimal representation without normalization and rounding off

Detailed Solution for Test: Floating Point Number- 2 - Question 3

The decimal number is 0.239 x 213
We have to find hexadecimal representation without normalization.
Biased exponent = 13 + 64 = 77
Representing 77 in binary
(77)10 = (1001101)2 
Representing mantissa in binary

(0.239)10 = 0.00111101000101 
Floating point representation is as follows:

Test: Floating Point Number- 2 - Question 4

Consider the following floating point format:

Mantissa is a pure fraction is sign-magnitude form.

Q. The normalized representation for the above format is specified as follows. The mantissa has an implicit 1 preceding the binary (radix) point. Assume that only 0’s are padded in while shifting a field. The normalized representation of the above number (0.239 x 213) is 

Detailed Solution for Test: Floating Point Number- 2 - Question 4

The decimal number is 0.239 x 213
We have to find hexadecimal representation with normalization.
Binary representation of 0.239 is 0.00111101000101 
∴ N is (0.00111101000101) x 213
After normalization we have 1.11101000101 x 210
Then, biased exponent - 10 + 64 = 74 Representating biased exponent 74 in binary (74)10 = (1001010)2
• Floating point representation of number is as follows-:

Test: Floating Point Number- 2 - Question 5

The addition of 4-bit, two’s complement, binary numbers 1101 and 0100 results in

Detailed Solution for Test: Floating Point Number- 2 - Question 5


No overflow

Test: Floating Point Number- 2 - Question 6

(C012.25)H -(10111001110.101)B =

Detailed Solution for Test: Floating Point Number- 2 - Question 6


Binary subtraction is like decimal subtraction:
0 - 0 = 0, 1 - 1 = 0, 1 - 0 = 1,
0 - 1 = 1 with 1 borrow.

Test: Floating Point Number- 2 - Question 7

The following bit pattern represents a floating point number in IEEE 754 single precision format:

The value of the number in decimal form is 

Detailed Solution for Test: Floating Point Number- 2 - Question 7

Sign bit is 1 implies number is negative. Exponent bits: 10000011 Exponent is added with 127 bias in IEEE single precision format.
So, Actual exponent
= 10000011 - 127 
= 131 - 127 = 4
Mantissa bits: 101000000000000000000000
In IEEE format, an implied 1 is before mantissa.
Hence the Number is -1.101*24
= - (11010)2 = - 26

Test: Floating Point Number- 2 - Question 8

In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to

Detailed Solution for Test: Floating Point Number- 2 - Question 8

An exponent of 0 together with a fraction of 0 with positive sign represents +0 which is a special value.

Test: Floating Point Number- 2 - Question 9

The two numbers given below are multiplied using the Booth’s algorithm.
Multiplicand: 0101101011101110
Multiplier: 0111011110111101

Q. How many additions/Subtractions are required for the multiplication of the above two numbers? 

Detailed Solution for Test: Floating Point Number- 2 - Question 9

Apply Booth’s algorithm:

4 additions and 4 substractions total 8 operations.

Test: Floating Point Number- 2 - Question 10

P is a 16-bit signed integer. The 2’s complement representation of P is (F87B)16. The 2's complement representation of 8*P is

Detailed Solution for Test: Floating Point Number- 2 - Question 10

2’s complement of P is given as (F87B)16
2’s complement of 8 x P = 23 x (F87B)16

Test: Floating Point Number- 2 - Question 11

The smallest integer that can be represent by and 8-bit number in 2’s complement form is

Detailed Solution for Test: Floating Point Number- 2 - Question 11

Range of 2’s complement no is
(-2n-1 to 2n-1 - 1)
So minimum no represents by 8 bit is
- 28 - 1 = - 128
maximum no represented by 8 bit is
28 - 1 - 1 = 127

Test: Floating Point Number- 2 - Question 12

The n-bit fixed-point representation of an unsigned real number X uses f bits for the fraction part. Let i = n - f. The range of decimal values for X in this representation is 

Detailed Solution for Test: Floating Point Number- 2 - Question 12

Let n = 5 bit
f = 2 bit
So i = 5 - 2 = 3 bit
Min value : 000.00
⇒ 0
Max value : 111.11
⇒ 7.75 
[2i - 2-f]
⇒ [23 - 2-2]
⇒ 8 - 0.25 = 7.75

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