Number Systems · Digital Logic · GATE CSE

Start Practice

Marks 1

GATE CSE 2024 Set 2
The format of a single-precision floating-point number as per the IEEE 754 standard is:table { width: 100%; border-collapse: collapse; margin: 20px 0;...
GATE CSE 2024 Set 1
Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers A and B are represented as ...
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 2021 Set 2
If x and y are two decimal digits and (0.1101)2 = (0.8xy5)10, the decimal value of x + y is ______...
GATE CSE 2021 Set 2
The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: sign ...
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 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
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 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 1
The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.
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 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 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
Sign extension is the step in
GATE CSE 2002
The $$2's$$ compliment representation of the decimal value $$-15$$ is
GATE CSE 2002
The decimal value $$0.25$$
GATE CSE 2000
The number $$43$$ in $$2's$$ complement representation is

Marks 2

GATE CSE 2024 Set 2
Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?
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 2022
Consider three floating point numbers A, B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single precision floating point forma...
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...
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12