GATE || DIGITAL LOGIC || NUMBER SYSTEM || PYQ (2010 TO 2025 )

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Question 1

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 require a minimum of: [GATE 2019 || MCQ ||1 Mark ]


  • n bits

  • n + 2 bits

  • n - 1 bits

  • n + 1 bits


Question 2

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 R2 gives an arithmetic overflow? [GATE|| 2022 MCQ || 2-mark ]

  • R1 = 1011 and R2 = 1110

  • R1 = 1100 and R2 = 1010

  • R1 = 0011 and R2 =0100

  • R1 = 1001 and R2 = 1111

Question 3

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 format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

RA=0xC1400000
RB=0x42100000
RC=0x41400000

Which one of the following is FALSE? [GATE || 2022 ||MCQ || 2-mark ]

  • A+C=0

  • C=A+B

  • B=3C

  • (B−C)>0

Question 4

A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is _____. [GATE || 2023 NAT || 1-mark]

  • 110

Question 5

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.
Which one of the following corresponds to the product of these numbers (i.e., P x Q), represented in the IEEE-754 single precision format? [GATE|| 2023 ||MCQ ||1-mark ]

  • 0x404C2EF4

  • 0x405C2EF4

  • 0xC15C2EF4

  • 0xC14C2EF4

Question 6

Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation ? [GATE||2024 ||SET2||MSQ ||1-mark ]

  • 64 in radix-10

  • 100 in radix-8

  • 50 in radix-16

  • 121 in radix-7

Question 7

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 . Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow? [GATE||2024 ||SET-1||MCQ ||1-mark ]

  • A + B

  • A - B

  • B - A

  • 2 * B

Question 8

he format of a single-precision floating-point number as per the IEEE 754 standard is:

Sign

(1 bit)

Exponent

(8 bits)

Mantissa

(23 bits)

Choose the largest floating-point number among the following options. [GATE || 2024||SET2|| MCQ ||1-mark ]

  • Sign - 0

    Exponent - 0111 1111

    Mantissa - 23 0’s

  • Sign - 0

    Exponent - 0111 1111

    Mantissa - 23 1’s

  • Sign - 0

    Exponent - 111 11110

    Mantissa - 23 1’s

  • Sign - 0

    Exponent - 1111 1111

    Mantissa - 23 1’s

Question 9

The following two signed 2's complement numbers (multiplicand M  and multiplier Q are being multiplied using Booth's algorithm:

M: 1100110111101101 and Q: 1010010010101010

The total number of addition and subtraction operations to be performed is _______ [GATE ||2025 SET2 || NAT || 2-mark]

  • 13

Question 10

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 ? [GATE|| 2025 SET1||MSQ ||1-mark]


  • 1000 1010 in 8 bits

  • 1111 1010 in 8 bits

  • 1000 0000 0000 1010 in 16 bits

  • 1111 1111 1111 1010 in 16 bits

There are 24 questions to complete.

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