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convert the hexidecimal number 0xC41C6800 in IEEE-754 single precision (32-bit) format, into decimal. write the answer...

convert the hexidecimal number 0xC41C6800 in IEEE-754 single precision (32-bit) format, into decimal. write the answer in decimal. please show all work

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Expert Solution

Answer:
--------
-625.625

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 C41C6800 to binary
C => 1100
4 => 0100
1 => 0001
C => 1100
6 => 0110
8 => 1000
0 => 0000
0 => 0000
So, in binary C41C6800 is 11000100000111000110100000000000
1 10001000 00111000110100000000000
sign bit is 1(-ve)
exp bits are 10001000
   => 10001000
   => 1x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+0x2^1+0x2^0
   => 1x128+0x64+0x32+0x16+1x8+0x4+0x2+0x1
   => 128+0+0+0+8+0+0+0
   => 136
in decimal it is 136
so, exponent/bias is 136-127 = 9
frac bits are 001110001101

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.001110001101 * 2^9
1.001110001101 in decimal is 1.221923828125
   => 1.001110001101
   => 1x2^0+0x2^-1+0x2^-2+1x2^-3+1x2^-4+1x2^-5+0x2^-6+0x2^-7+0x2^-8+1x2^-9+1x2^-10+0x2^-11+1x2^-12
   => 1x1+0x0.5+0x0.25+1x0.125+1x0.0625+1x0.03125+0x0.015625+0x0.0078125+0x0.00390625+1x0.001953125+1x0.0009765625+0x0.00048828125+1x0.000244140625
   => 1+0.0+0.0+0.125+0.0625+0.03125+0.0+0.0+0.0+0.001953125+0.0009765625+0.0+0.000244140625
   => 1.221923828125
so, 1.221923828125 * 2^9 in decimal is 625.625
so, 11000100000111000110100000000000 in IEEE-754 single precision format is -625.625
Answer: -625.625


venereology answered 2 hours ago
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