edited by
9,650 views
12 12 votes

What is the decimal value of the floating-point number $C1D00000$ (hexadecimal notation)? (Assume $32$-bit, single precision floating point $\text{IEEE}$ representation)

  1. $28$
  2. $-15$
  3. $-26$
  4. $-28$

1 Answer

Best answer
21 21 votes

C1D00000 = 1100 0001 1101 0000……0000

In IEEE representation for single precision floating point numbers, first bit is for sign, next 8 bits for exponent and last 23 bits for mantissa which excludes the implicit "1" before ".", unless the number is not normalized (happens only when exponent is 0 and mantissa is non zero).

First bit = sign bit = 1, so number is negative

exponent $= 131 - 127 = 4$ (127 is the bias in IEEE representation). 

significant $= 1. 101\underbrace{000\dots 0}_{\text{20 0's}} \\=(1)2^0 + (1)2^{-1} + (0)2^{-2 }+ (1)2^{-3} \\= 1 + 1/2 + 0 + 1/8 = 13/8$

hence we finally get decimal value

$= \text{sign} \times  2^{\text{exponent}} \times \text{significant} = -26$.

selected by
Answer:
Position:
Show:

Related questions

28 28 votes
6 6 answers
22.0k
22.0k views
Arjun asked Feb 16, 2024
22,044 views
​​The format of a single-precision floating-point number as per the $\text{IEEE 754}$ standard is:$$\begin{array}{|l|l|l|}\hline \textbf{Sign} & \textbf{Exponent} & \tex...
45 45 votes
6 6 answers
29.5k
29.5k views
admin asked Feb 15, 2023
29,537 views
Consider the $\textsf{IEEE-754}$ single precision floating point numbers $\text{P} = \textsf{0xC1800000}$ and $\text{Q} = \textsf{0x3F5C2EF4}.$Which one of the following ...
27 27 votes
5 5 answers
19.6k
19.6k views
Arjun asked Feb 15, 2022
19,557 views
Consider three floating point numbers $\textit{A, B}$ and $\textit{C}$ stored in registers $\text{R}_{\text{A}}, \text{R}_{\text{B}}$ and $\text{R}_{\text{C}},$ respectiv...
44 44 votes
5 answers 5 answers
21.0k
21.0k views
Arjun asked Feb 18, 2021
21,001 views
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ standard is as follows:$$\begin{array}{|c|c|c|} \hline \tex...