Convert 0xCD001234 from IEEE-754 hexadecimal to single-precision floating point format. Please show every single detail for...

Convert 0xCD001234 from IEEE-754 hexadecimal to single-precision floating point format.
Please show every single detail for upvote.
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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 CD001234 to binary
C => 1100
D => 1101
0 => 0000
0 => 0000
1 => 0001
2 => 0010
3 => 0011
4 => 0100
So, in binary CD001234 is 11001101000000000001001000110100
11001101000000000001001000110100
1 10011010 00000000001001000110100
sign bit is 1(-ve)
exp bits are 10011010
   => 10011010
   => 1x2^7+0x2^6+0x2^5+1x2^4+1x2^3+0x2^2+1x2^1+0x2^0
   => 1x128+0x64+0x32+1x16+1x8+0x4+1x2+0x1
   => 128+0+0+16+8+0+2+0
   => 154
in decimal it is 154
so, exponent/bias is 154-127 = 27
frac bits are 000000000010010001101

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.000000000010010001101 * 2^27
1.000000000010010001101 in decimal is 1.0005555152893066
   => 1.000000000010010001101
   => 1x2^0+0x2^-1+0x2^-2+0x2^-3+0x2^-4+0x2^-5+0x2^-6+0x2^-7+0x2^-8+0x2^-9+0x2^-10+1x2^-11+0x2^-12+0x2^-13+1x2^-14+0x2^-15+0x2^-16+0x2^-17+1x2^-18+1x2^-19+0x2^-20+1x2^-21
   => 1x1+0x0.5+0x0.25+0x0.125+0x0.0625+0x0.03125+0x0.015625+0x0.0078125+0x0.00390625+0x0.001953125+0x0.0009765625+1x0.00048828125+0x0.000244140625+0x0.0001220703125+1x6.103515625e-05+0x3.0517578125e-05+0x1.52587890625e-05+0x7.62939453125e-06+1x3.814697265625e-06+1x1.9073486328125e-06+0x9.5367431640625e-07+1x4.76837158203125e-07
   => 1+0.0+0.0+0.0+0.0+0.0+0.0+0.0+0.0+0.0+0.0+0.00048828125+0.0+0.0+6.103515625e-05+0.0+0.0+0.0+3.814697265625e-06+1.9073486328125e-06+0.0+4.76837158203125e-07
   => 1.0005555152893066
so, 1.0005555152893066 * 2^27 in decimal is 134292288.0
so, 11001101000000000001001000110100 in IEEE-754 single precision format is -134292288.0
Answer: -134292288.0

venereology answered 5 months ago

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