GATE CSE
Digital Logic
Number Systems
Previous Years Questions

## Marks 1

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...
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...
In 16-bit 2's complement representation, the decimal number -28 is :
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 ...
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...
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 ...
The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.
Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is ____...
The base (or radix) of the number system such that the following equation holds is __________ $${{312} \over {20}} = 13.1$$
The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is
$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement rep...
$${\left( {1217} \right)_8}$$ is equivalent to
$${73_x}$$ (in base $$-$$ $$x$$ number system) is equal to $${54_y}$$ (in base $$-y$$ number system), the possible values of $$x$$ and $$y$$ are
Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011?$$
The decimal value $$0.25$$
The $$2's$$ compliment representation of the decimal value $$-15$$ is
Sign extension is the step in
The number $$43$$ in $$2's$$ complement representation is

## Marks 2

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...
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S: 1 E:   10000001...
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...
Consider the unsigned $$8$$-bit fixed point binary number representation below $${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\... Consider the equation$${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$where$$x$$and$$y$$are unknown. The number of possible solutions is ___... Let$$A=11111010$$and$$B=00001010$$be two$$8$$-bit$$2's$$complement numbers. Their product in$$2's$$complement is The$$2's$$complement representation of$${\left( { - 539} \right)_{10}}$$in hexadecimal is Zero has two representations in: Given$$\sqrt {\left( {224} \right),} = {\left( {13} \right)_r},$$The value of the radix'$$r$$is: Consider the number given by the decimal expression.$${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$The number of$$1's in the unsigned bi...
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