# Number Systems · Digital Logic · GATE CSE

Start Practice## Marks 1

GATE CSE 2023

A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is ____________.

GATE CSE 2022

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and...

GATE CSE 2022

Consider three floating points numbers A, B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single precision floating point form...

GATE CSE 2019

In 16-bit 2's complement representation, the decimal number -28 is :

GATE CSE 2019

Consider Z = X - Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of ...

GATE CSE 2016 Set 2

Consider an eight-bit ripple-carry adder for computing the sum of $$A$$ and $$B,$$ where $$A$$ and $$B$$ are integers represented in $$2’s$$ complemen...

GATE CSE 2016 Set 2

Let $$X$$ be the number of distinct $$16$$-bit integers in $$2’s$$ complement representation. Let $$Y$$ be the number of distinct $$16$$-bit integers ...

GATE CSE 2016 Set 1

The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal
representation is ____________.

GATE CSE 2014 Set 1

The base (or radix) of the number system such that the following equation holds is __________
$${{312} \over {20}} = 13.1$$

GATE CSE 2014 Set 2

Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is ____...

GATE CSE 2013

The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is

GATE CSE 2010

$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement rep...

GATE CSE 2009

$${\left( {1217} \right)_8}$$ is equivalent to

GATE CSE 2004

$${73_x}$$ (in base $$-$$ $$x$$ number system) is equal to $${54_y}$$ (in base $$-y$$ number system), the possible values of $$x$$ and $$y$$ are

GATE CSE 2003

Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011?$$

GATE CSE 2002

The decimal value $$0.25$$

GATE CSE 2002

Sign extension is the step in

GATE CSE 2002

The $$2's$$ compliment representation of the decimal value $$-15$$ is

GATE CSE 2000

The number $$43$$ in $$2's$$ complement representation is

## Marks 2

GATE CSE 2023

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.
Which one of the following corresponds to the product of ...

GATE CSE 2021 Set 1

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8d7d6d5c8d4d3d2c4d1c2c1, where the data bits and the check bits ar...

GATE CSE 2021 Set 1

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

GATE CSE 2021 Set 1

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.
S: 1 E: 10000001...

GATE CSE 2020

Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values...

GATE CSE 2018

Consider the unsigned $$8$$-bit fixed point binary number representation below
$$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\...

GATE CSE 2015 Set 3

Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The number of possible solutions is ___...

GATE CSE 2004

Let $$A=1111$$ $$1010$$ and $$B=0000$$ $$1010$$ be two $$8$$-bit $$2's$$ complement numbers. Their product in $$2's$$ complement is

GATE CSE 2001

The $$2's$$ complement representation of $${\left( { - 539} \right)_{10}}$$ in hexadecimal is

GATE CSE 1999

Zero has two representations in:

GATE CSE 1997

Given $$\sqrt {\left( {224} \right),} = {\left( {13} \right)_r},$$
The value of the radix' $$r$$ is:

GATE CSE 1990

Consider the number given by the decimal expression.
$${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$
The number of $$1's$$ in the unsigned bi...