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GATE and NET question on IEEE – 754

Gate questions CS - 2014

The value of a floating type variable is represented using the single-precision 32-bit format. IEEE 754 standard uses 1 bit for sign, 8 bits for the biased exponent, and 23 bits for mantissa. A float type variable is assigned the decimal value of -14.25. The representation of X in hexadecimal notation is

(A) C1640000H                   

(B) 416C0000H                   

(C) 416C0000H

(D) C16C0000H

You should know:

Before seeing the questions please follow the previous chapter: IEEE – 754

Solution:

Exponent is 3

# Because single precision is Exponent is excess 127.

So,

The number in hexadecimal notation is  C1640000H,

So, option (A) is correct.

UGC NET questions CS – 2014-DEC

The range of representable normalized numbers in the floating-point binary fractional representation in a 32- bit word with 1-bit sign, 8-bit excess 128 biased exponent, and the 23-bit mantissa is

You should know:

Before seeing the questions please follow the previous chapter: IEEE – 754

Solution:

The smallest number will be E-128

Maximum or largest number will be

Range of representable normalized numbers:   

So, option (D) is correct.

GATE questions CS – 2012

The decimal value 0.5 in IEEE single-precision format has

(A) fraction bits 000…000 and exponent value 0

(B) fraction bits 000…000and exponent value -1

(C) fraction bits 100…000 and exponent value 0

(D) no exact representation

You should know:

Before seeing the questions please follow the previous chapter: IEEE – 754

Solution:

So, fraction bits or mantissa will be 000…000 and exponent value -1.

So, option (B) is correct.

Moreover, its representation in 32 – bits format will be.

Biased exponent = -1+127 = 126

(Because single precision is Exponent is excess 127)

And its hexadecimal representation will be