GATE CS 2024 Set 2 | Question 14

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

Sign
(1bit)

Exponent
(8 bits)

Mantissa
(23 bits)

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

Option A:
Sign Exponent Mantissa
0 0111 1111 1111 1111 1111 1111 1111 111
Option B:
Sign Exponent Mantissa
0 1111 1110 1111 1111 1111 1111 1111 111
(correct)
Option C:
Sign Exponent Mantissa
0 1111 1111 1111 1111 1111 1111 1111 111
Option D:
Sign Exponent Mantissa
0 0111 1111 0000 0000 0000 0000 0000 000

Sign	Exponent	Mantissa
0	0111 1111	1111 1111 1111 1111 1111 111

Sign	Exponent	Mantissa
0	1111 1110	1111 1111 1111 1111 1111 111

Sign	Exponent	Mantissa
0	1111 1111	1111 1111 1111 1111 1111 111

Sign	Exponent	Mantissa
0	0111 1111	0000 0000 0000 0000 0000 000

Answer

(B)

All four have sign bit 0, so compare their values using the exponent bias of 127.

A: exponent 0111 1111 is 127, so the value is \((2 - 2^{-23}) \times 2^{0}\), just under 2.
B: exponent 1111 1110 is 254, so the value is \((2 - 2^{-23}) \times 2^{127}\), about \(3.4 \times 10^{38}\).
C: an all-ones exponent is reserved. With a non-zero mantissa the pattern means NaN (not a number), which has no value to compare.
D: exponent 127 with a zero mantissa is exactly 1.

B is in fact the largest finite single-precision number, so it is the largest option.

Answer: B