Number Representations and Computer Arithmetic: GATE CS previous year questions (Digital Logic)

GATE CS 2026 Set 1MSQ1 markEasy (estimate)
GATE CS 2026 Set 1, Q.22
Consider the 8-bit signed integers $X$ , $Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows…
Number Representations and Computer Arithmetic
GATE CS 2026 Set 2MSQ1 markEasy (estimate)
GATE CS 2026 Set 2, Q.28
In a system, numbers are represented using 4-bit two's complement form. Consider four numbers $N_{1} = 1011$ , $N_{2} = 1101$ , $N_{3} = 1010$ and $N_{4} = 1001$ in the system. Which of t...
Number Representations and Computer Arithmetic
GATE CS 2026 Set 2NAT1 markEasy (estimate)
GATE CS 2026 Set 2, Q.34
The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal representation is ________. (rounded off to two decimal places)
Number Representations and Computer Arithmetic
GATE CS 2025 Set 1MSQ1 markEasy (estimate)
GATE CS 2025 Set 1, Q.25
The number $- 6$ can be represented as $1010$ in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $- 6$ ?
Number Representations and Computer Arithmetic
GATE CS 2025 Set 2NAT1 markEasy (estimate)
GATE CS 2025 Set 2, Q.32
The following two signed 2's complement numbers (multiplicand M and multiplier Q) are being multiplied using Booth's algorithm: M: 1100 1101 1110 1101 and Q…
ALU, Datapath and Control Unit · Number Representations and Computer Arithmetic
GATE CS 2025 Set 2MSQ2 marksEasy (estimate)
GATE CS 2025 Set 2, Q.49
Three floating point numbers $X, Y,$ and $Z$ are stored in three registers $R_{X}, R_{Y},$ and $R_{Z}$ , respectively in IEEE 754 single precision format as given below in hexadecimal:...
ALU, Datapath and Control Unit · Number Representations and Computer Arithmetic
GATE CS 2024 Set 1MCQ1 markEasy (estimate)
GATE CS 2024 Set 1, Q.13
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 $A = 01010$ and $B = 11010$ ...
Number Representations and Computer Arithmetic
GATE CS 2024 Set 2MCQ1 markEasy (estimate)
GATE CS 2024 Set 2, Q.14
The format of a single-precision floating-point number as per the IEEE 754 standard is: Sign Exponent Mantissa (1 bit) (8 bits) (23 bits) Choose the largest floating-point numbe...
ALU, Datapath and Control Unit · Number Representations and Computer Arithmetic
GATE CS 2024 Set 2MSQ2 marksEasy (estimate)
GATE CS 2024 Set 2, Q.49
Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?
Number Representations and Computer Arithmetic
GATE CS 2023NAT1 markEasy (estimate)
GATE CS 2023, Q.32
A particular number is written as $132$ in radix- $4$ representation. The same number in radix- $5$ representation is _______.
Number Representations and Computer Arithmetic
GATE CS 2022MCQ1 markEasy (estimate)
GATE CS 2022, Q.18
Let $R_{1}$ and $R_{2}$ be two 4-bit registers that store numbers in 2's complement form. For the operation $R_{1} + R_{2}$ , which one of the following values of $R_{1}$ and $R_{2}$ gives a...
Number Representations and Computer Arithmetic
GATE CS 2021 Set 1MCQ1 markEasy (estimate)
GATE CS 2021 Set 1, Q.16 (CS Q.6)
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
Number Representations and Computer Arithmetic
GATE CS 2021 Set 1NAT1 markEasy (estimate)
GATE CS 2021 Set 1, Q.34 (CS Q.24)
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S: 1 E: 10000001 F: 11110000000000000000000 Here S, E an...
Number Representations and Computer Arithmetic
GATE CS 2021 Set 2MCQ1 markMedium (estimate)
GATE CS 2021 Set 2, Q.14 (CS Q.4)
The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: Sign bit: 1 bit, Exponent: 8 bits, Mantissa: 23 bit...
Number Representations and Computer Arithmetic
GATE CS 2021 Set 2NAT1 markEasy (estimate)
GATE CS 2021 Set 2, Q.28 (CS Q.18)
If $x$ and $y$ are two decimal digits and $(0.1101)_{2} = (0.8 x y 5)_{10}$ , the decimal value of $x + y$ is ______.
Number Representations and Computer Arithmetic
GATE CS 2020MCQ2 marksMedium (estimate)
GATE CS 2020, Q.39 (CS Q.29)
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 (in hexadecimal notation)...
Number Representations and Computer Arithmetic
GATE CS 2020NAT2 marksMedium (estimate)
GATE CS 2020, Q.54 (CS Q.44)
A processor has 64 registers and uses 16-bit instruction format. It has two types of instructions: I-type and R-type. Each I-type instruction contains an opcode, a register name...
Instruction Pipelining and Hazards · Number Representations and Computer Arithmetic
GATE CS 2019MCQ1 markEasy (estimate)
GATE CS 2019, Q.14 (CS Q.4)
In 16-bit 2's complement representation, the decimal number $- 28$ is:
Number Representations and Computer Arithmetic
GATE CS 2019MCQ1 markEasy (estimate)
GATE CS 2019, Q.18 (CS Q.8)
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 $Z$ would requi...
Number Representations and Computer Arithmetic
GATE CS 2018MCQ2 marksEasy (estimate)
GATE CS 2018, Q.43 (CS Q.33)
Consider the unsigned 8-bit fixed point binary number representation below, $b_{7} b_{6} b_{5} b_{4} b_{3} . b_{2} b_{1} b_{0}$ where the position of the binary point...
Number Representations and Computer Arithmetic
GATE CS 2017 Set 1MCQ1 markEasy (estimate)
GATE CS 2017 Set 1, Q.7 (CS Q.7)
The $n$ -bit fixed-point representation of an unsigned real number $X$ uses $f$ bits for the fraction part. Let $i = n - f$ . The range of decimal values for $X$ in this represent...
Number Representations and Computer Arithmetic
GATE CS 2017 Set 1MCQ1 markEasy (estimate)
GATE CS 2017 Set 1, Q.9 (CS Q.9)
When two 8-bit numbers $A_{7} \dots A_{0}$ and $B_{7} \dots B_{0}$ in 2's complement representation (with $A_{0}$ and $B_{0}$ as the least significant bits) are added using a ripple-carry a...
ALU, Datapath and Control Unit · Number Representations and Computer Arithmetic
GATE CS 2017 Set 2MCQ1 markEasy (estimate)
GATE CS 2017 Set 2, Q.1 (CS Q.1)
The representation of the value of a 16-bit unsigned integer $Y$ in hexadecimal number system is $BCA9$ . The representation of the value of $Y$ in octal number system is
Number Representations and Computer Arithmetic
GATE CS 2017 Set 2MCQ1 markMedium (estimate)
GATE CS 2017 Set 2, Q.12 (CS Q.12)
Given the following binary number in 32-bit (single precision) IEEE-754 format: 00111110011011010000000000000000 The decimal value closest to this floating-point number is
Number Representations and Computer Arithmetic
GATE CS 2017 Set 2NAT1 markEasy (estimate)
GATE CS 2017 Set 2, Q.24 (CS Q.24)
Consider a quadratic equation $x^{2} - 13 x + 36 = 0$ with coefficients in a base $b$ . The solutions of this equation in the same base $b$ are $x = 5$ and $x = 6$ . Then $b =$
Number Representations and Computer Arithmetic
GATE CS 2016 Set 1NAT1 markEasy (estimate)
GATE CS 2016 Set 1, Q.17 (CS Q.7)
The 16-bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is _____.
Number Representations and Computer Arithmetic
GATE CS 2016 Set 1MCQ2 marksMedium (estimate)
GATE CS 2016 Set 1, Q.43 (CS Q.33)
Consider a carry lookahead adder for adding two $n$ -bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is
Number Representations and Computer Arithmetic
GATE CS 2016 Set 2NAT1 markMedium (estimate)
GATE CS 2016 Set 2, Q.17 (CS Q.7)
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 complement form. If the decimal value of $A$ is...
Number Representations and Computer Arithmetic
GATE CS 2016 Set 2NAT1 markEasy (estimate)
GATE CS 2016 Set 2, Q.19 (CS Q.9)
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 in sign magnitude representation. Then…
Number Representations and Computer Arithmetic
GATE CS 2015 Set 3NAT2 marksMedium (estimate)
GATE CS 2015 Set 3, Q.45 (CS Q.35)
Consider the equation $(43)_{x} = (y 3)_{8}$ where $x$ and $y$ are unknown. The number of possible solutions is _____.
Number Representations and Computer Arithmetic
GATE CS 2014 Set 1NAT1 markEasy (estimate)
GATE CS 2014 Set 1, Q.18 (CS Q.8)
The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$
Number Representations and Computer Arithmetic
GATE CS 2014 Set 2NAT1 markMedium (estimate)
GATE CS 2014 Set 2, Q.18 (CS Q.8)
Consider the equation $(123)_{5} = (x 8)_{y}$ with $x$ and $y$ as unknown. The number of possible solutions is _____.
Number Representations and Computer Arithmetic
GATE CS 2014 Set 2MCQ2 marksEasy (estimate)
GATE CS 2014 Set 2, Q.55 (CS Q.45)
The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased expone...
Number Representations and Computer Arithmetic
GATE CS 2013MCQ1 markEasy (estimate)
GATE CS 2013, Q.4 (CS Q.4)
The smallest integer that can be represented by an 8-bit number in 2’s complement form is
Number Representations and Computer Arithmetic
GATE CS 2012MCQ1 markEasy (estimate)
GATE CS 2012, Q.7 (CS Q.7)
The decimal value 0.5 in IEEE single precision floating point representation has
Number Representations and Computer Arithmetic

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