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GATE CSE
Number Systems
Digital Logic
Previous Years Questions
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Marks 1
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Consider three floating points numbers A, B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single...
GATE CSE 2022
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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 ...
GATE CSE 2022
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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 ov...
GATE CSE 2019
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In 16-bit 2's complement representation, the decimal number -28 is :
GATE CSE 2019
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Let $$X$$ be the number of distinct $$16$$-bit integers in $$2’s$$ complement representation. Let $$Y$$ be the number of...
GATE CSE 2016 Set 2
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Consider an eight-bit ripple-carry adder for computing the sum of $$A$$ and $$B,$$ where $$A$$ and $$B$$ are integers re...
GATE CSE 2016 Set 2
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The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal repre...
GATE CSE 2016 Set 1
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Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number...
GATE CSE 2014 Set 2
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The base (or radix) of the number system such that the following equation holds is __________ $${{312} \over {20}} = 13....
GATE CSE 2014 Set 1
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The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is
GATE CSE 2013
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$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$...
GATE CSE 2010
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$${\left( {1217} \right)_8}$$ is equivalent to
GATE CSE 2009
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$${73_x}$$ (in base $$-$$ $$x$$ number system) is equal to $${54_y}$$ (in base $$-y$$ number system), the possible value...
GATE CSE 2004
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Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011...
GATE CSE 2003
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Sign extension is the step in
GATE CSE 2002
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The $$2's$$ compliment representation of the decimal value $$-15$$ is
GATE CSE 2002
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The decimal value $$0.25$$
GATE CSE 2002
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The number $$43$$ in $$2's$$ complement representation is
GATE CSE 2000
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Marks 2
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Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127....
GATE CSE 2021 Set 1
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Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
GATE CSE 2021 Set 1
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Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8d7d6d5c8d4d3d2c4d1c2c1, where the d...
GATE CSE 2021 Set 1
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Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume tha...
GATE CSE 2020
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Consider the unsigned $$8$$-bit fixed point binary number representation below $$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{...
GATE CSE 2018
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Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The numbe...
GATE CSE 2015 Set 3
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Let $$A=1111$$ $$1010$$ and $$B=0000$$ $$1010$$ be two $$8$$-bit $$2's$$ complement numbers. Their product in $$2's$$ co...
GATE CSE 2004
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The $$2's$$ complement representation of $${\left( { - 539} \right)_{10}}$$ in hexadecimal is
GATE CSE 2001
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Zero has two representations in:
GATE CSE 1999
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Given $$\sqrt {\left( {224} \right),} = {\left( {13} \right)_r},$$ The value of the radix' $$r$$ is:
GATE CSE 1997
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Consider the number given by the decimal expression. $${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$ The number...
GATE CSE 1990
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