GATE CSE 2024 | Set 2 | Question: 4

Question

​​The format of a single-precision floating-point number as per the $\text{IEEE 754}$ standard is:

Sign	Exponent	Mantissa
$(1 \mathrm{bit})$	$(8 \mathrm{bits})$	$(23 \mathrm{bits})$

Choose the largest floating-point number among the following options.​​​​​​​​​​​​​​​​​​​​​    

Sign	Exponent	Mantissa
$0$	$01111111$	$1111 1111 1111 1111 1111 111$

Sign	Exponent	Mantissa
$0$	$11111110$	$1111 1111 1111 1111 1111 111$

Sign	Exponent	Mantissa
$0$	$11111111$	$11111111111111111111111$

Sign	Exponent	Mantissa
$0$	$01111111$	$00000000000000000000000$

Comments

Note: Infinity is NOT a number. See Here.

Answer 1

B.

Setting exponent as 11111110. Also mantissa will be all 1's. This combination will result in the largest FPN. Note that here the LSB is not 1. Setting all exponent bits to 1 will result in a spcl notation which is reserved in IEEE 754 format.