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# GATE CS 2021 : Digital Logic 4 (App update required to attempt this test)

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Question 1

Consider a 32-bit register which stores floating point number in IEEE single precision format. The value of the number ____ in decimal if 32-bit sequence is given as

where first block represents sign bit, second block represent biased exponent value and third block represent value of mantissa.

Question 2

Consider a 16-bit register of following format to store a Floating Point number:

Mantissa, M is denoted as normalized signed magnitude fraction.

Exponent, E is expressed in excess-64 form.

Base of system is

Let's say 2^{a} is the difference(q-p) between first smallest positive number, say p and 2nd smallest positive number, say q. Then what is the value of a?

Question 3

The decimal equivalents of 01440000 a 32- bit hexadecimal representation of IEEE single-precision floating point number is

Question 4

Consider the following floating-point format:

S : Sign bit

E: Exponent

M : Mantissa

The value of floating point number in this system is,

V = (-1)^{s} ×2E^{—127} × 1.F

Then what is the corresponding decimal value if the floating point stored is: 3F800000

Question 5

IEEE 754 single precision format is used to store floating point numbers. Let X be the smallest number representable using implicit normalized form and Y is largest number representable using fractional form. Then the value of (X-Y)*2

^{150}is ______.Question 6

The decimal value -45.25 is converted to IEEE754 single precision floating point representation. Calculate the number of 1’s that appear in the representation.

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Sep 12GATE & PSU CS

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