Question

convert 0xC2000000 into IEEE-754 single precision decimal format.

Answer 1

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 C2000000 to binary
C => 1100
2 => 0010
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
So, in binary C2000000 is 11000010000000000000000000000000
11000010000000000000000000000000
1 10000100 00000000000000000000000
sign bit is 1(-ve)
exp bits are 10000100
   => 10000100
   => 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+0x2^1+0x2^0
   => 1x128+0x64+0x32+0x16+0x8+1x4+0x2+0x1
   => 128+0+0+0+0+4+0+0
   => 132
in decimal it is 132
so, exponent/bias is 132-127 = 5
frac bits are

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1. * 2^5
1. in decimal is 1
   => 1.
   => 1x2^0
   => 1x1
   => 1
   => 1
so, 1 * 2^5 in decimal is 32
so, 11000010000000000000000000000000 in IEEE-754 single precision format is -32
Answer: -32