GATE || Digital Logic || PYQ || 2026 || Module 1: Number System

Consider the real valued variables X, Y and Z represented using the IEEE -754 single precision floating-point format. The binary representations of X and Y in hexadecimal notation are as follows:

X: 35C00000
Y: 34A00000

Let Z = X + Y.

Which one of the following is the binary representation of Z, in hexadecimal notation? [GATE ||2026 SET1 || MCQ || 1-mark]

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: 10110100
Y: 01001100

Which of the following operations to compute Z result(s) in an arithmetic overflow? [GATE ||2026 SET1 || MSQ || 1-mark]

In a system, numbers are represented using 4- bit two's complement form. Consider four numbers

N1 = 1011, N2 = 1101, N3 = 1010 and N4 = 1001 in the system.

Which of the following operations will result in arithmetic overflow? [GATE ||2026 SET2 || MSQ || 1-mark]

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). [GATE ||2026 SET2 || NAT || 1-mark]