GATE CS Number Representations (Fixed and Floating Point) questions

Practise Number Representations (Fixed and Floating Point) questions for GATE CS. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

20 on this page

SubjectTopicYearType

Two numbers are chosen independently and uniformly at random from the set

\{1,2,\ldots,13\}.

The probability (rounded off to

3

decimal places) that their

4\text{-bit}

(unsigned) binary representations have the same most significant bit is ___________.

Consider the unsigned 8-bit fixed point binary number representation, below,

b_7 \: \: b_6 \: \: b_5 \: \: b_4 \: \: b_3 \: \: \cdot b_2 \: \: b_1 \: \: b_0

where the position of the primary point is between

b_3

b_2

b_7

is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the …

8\text{-bit}

A_{7}\cdots A_{0}

B_{7}\cdots B_{0}

2

's complement representation (with

A_{0}

B_{0}

as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are

S_{7}\cdots S_{0}

and the carry bits are

C_{7}\cdots C_{0}

. An overflow is said to have occurred if

The n-bit fixed-point representation of an unsigned real number

X

f

bits for the fraction part. Let

i = n-f

. The range of decimal values for

X

in this representation is

Given the following binary number in

32

-bit (single precision)

\text{IEEE-754}

\large 00111110011011010000000000000000

The decimal value closest to this floating-point number is :

The representation of the value of a

16\text{-bit}

unsigned integer

X

in hexadecimal number system is

\textsf{BCA9}

. The representation of the value of

X

in octal number system is

16\text{-bit}\;2's

complement representation of an integer is

1111 \quad 1111 \quad 1111 \quad 0101;

its decimal representation is ____________

X

be the number of distinct

16

-bit integers in

2's

complement representation. Let

Y

be the number of distinct

16

-bit integers in sign magnitude representation Then

X - Y

Consider the equation

(43)_x = (y3)_8

x

y

are unknown. The number of possible solutions is _____

The base (or radix) of the number system such that the following equation holds is____________.

\frac{312}{20} = 13.1

\text{float}

type variable is represented using the single-precision

\text{32-bit}

floating point format of

\text{IEEE-754}

standard that uses

1

\text{bit}

\text{8 bits}

for biased exponent and

\text{23 bits}

for the mantissa. A

\text{float}

X

is assigned the decimal value of …

Consider the equation

(123)_5=(x8)_y

x

y

as unknown. The number of possible solutions is _____ .

The smallest integer that can be represented by an

8\text{-bit}

2's

complement form is

The decimal value

0.5

in IEEE single precision floating point representation has

P

16

-bit signed integer. The

2

's complement representation of

P

(F87B)_{16}

2

's complement representation of

8\times P

(1217)_8

is equivalent to

r

denote number system radix. The only value(s) of

r

that satisfy the equation

\sqrt{121_r}={11}_r

In the IEEE floating point representation the hexadecimal value

0\text{x}00000000

Consider numbers represented in 4-bit Gray code. Let

h_{3}h_{2}h_{1}h_{0}

be the Gray code representation of a number

n

g_{3}g_{2}g_{1}g_{0}

be the Gray code of

(n+1)(modulo 16)

value of the number. Which one of the following functions is correct?

We consider the addition of two

2's

complement numbers

b_{n-1}b_{n-2}\dots b_{0}

a_{n-1}a_{n-2}\dots a_{0}

. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by

c_{n-1}c_{n-2}\dots c_{0}

and the carry-out by

c_{out}

. Which one of the following options correctly identifies the overflow …