The GATE Grind

GATE Computer Organization and Architecture: Number Representation and Floating Point Arithmetic – Previous Year Questions

12 GATE previous year questions on Number Representation and Floating Point Arithmetic (Computer Organization and Architecture, Computer Science) with answers and explanations, from every paper.

  1. GATE 2018 CS Q43 (2 marks, Multiple choice) – Consider the unsigned 8-bit fixed point binary number representation below, b 7b 6b 5b 4b 3.b 2b 1b 0 where the position of the binary point is…
  2. GATE 2026 CS (CS2) Q28 (1 mark, Multiple select) – 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. Which of the…
  3. GATE 2026 CS (CS2) Q34 (1 mark, Numerical answer) – The 32-bit IEEE 754 single-precision representation of a number is `0xC2710000`. The number in decimal representation is . (rounded off to two decimal…
  4. GATE 2026 CS (CS1) Q22 (1 mark, Multiple select) – 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: X:…
  5. GATE 2026 CS (CS1) Q36 (2 marks, Multiple choice) – Consider the real valued variables X, Y and Z represented using the IEEE 754 single-precision floating-point format. The binary representations of X…
  6. GATE 2025 CS (CS2) Q32 (1 mark, Numerical answer) – 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…
  7. GATE 2025 CS (CS2) Q49 (2 marks, Multiple select) – 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…
  8. GATE 2024 CS (CS2) Q14 (1 mark, Multiple choice) – The 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…
  9. GATE 2024 CS (CS1) Q13 (1 mark, Multiple choice) – 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…
  10. GATE 2023 CS Q45 (2 marks, Multiple choice) – Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4. Which one of the following corresponds to the product of…
  11. GATE 2022 CS Q41 (2 marks, Multiple choice) – Consider three floating point numbers A, B and C stored in registers R A, R B and R C, respectively as per IEEE-754 single precision floating point…
  12. GATE 2020 CS Q39 (2 marks, Multiple choice) – 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…