Question

Convert from 32-bit IEEE 754 Floating Point Standard (in hexadecimal) to decimal: 410C0000, with the following layout: first bit is sign bit, next 8 bits is exponent field, and remaining 23 bits is mantissa field; result is to be rounded up if needed.

answer choices

9.125

8.75

7.75

4.625

6.3125

Answer 1

Answer:
----------
b)  8.75

Explanation:
-------------
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting 410C0000 to binary
4 => 0100
1 => 0001
0 => 0000
C => 1100
0 => 0000
0 => 0000
0 => 0000
0 => 0000
So, in binary 410C0000 is 01000001000011000000000000000000
0 10000010 00011000000000000000000
sign bit is 0(+ve)
exp bits are 10000010
   => 10000010
   => 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+1x2^1+0x2^0
   => 1x128+0x64+0x32+0x16+0x8+0x4+1x2+0x1
   => 128+0+0+0+0+0+2+0
   => 130
in decimal it is 130
so, exponent/bias is 130-127 = 3
frac bits are 00011

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.00011 * 2^3
1.00011 in decimal is 1.09375
   => 1.00011
   => 1x2^0+0x2^-1+0x2^-2+0x2^-3+1x2^-4+1x2^-5
   => 1x1+0x0.5+0x0.25+0x0.125+1x0.0625+1x0.03125
   => 1+0.0+0.0+0.0+0.0625+0.03125
   => 1.09375
so, 1.09375 * 2^3 in decimal is 8.75
so, 01000001000011000000000000000000 in IEEE-754 single precision format is 8.75
Answer: 8.75