In this question, you are provided with an IEEE-754 floating-point number in the form of 8...

In this question, you are provided with an IEEE-754 floating-point number in the form of 8 hexadecimal digits.

You are asked to decode this value into its decimal representation.

You MUST report your answer as a real number.

Do NOT use scientific notation.

Do NOT round or truncate your answer.

Do NOT add any spaces or commas to your answer.

If the converted number is positive, do NOT add the plus sign.

Convert, i.e., decode, 0x48801002 from the 32-bit single-precision IEEE-754 FP representation into decimal representation.

Expert Solution

Answer: 262272.0625

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 48801002 to binary
4 => 0100
8 => 1000
8 => 1000
0 => 0000
1 => 0001
0 => 0000
0 => 0000
2 => 0010
So, in binary 48801002 is 01001000100000000001000000000010
01001000100000000001000000000010
0 10010001 00000000001000000000010
sign bit is 0(+ve)
exp bits are 10010001
   => 10010001
   => 1x2^7+0x2^6+0x2^5+1x2^4+0x2^3+0x2^2+0x2^1+1x2^0
   => 1x128+0x64+0x32+1x16+0x8+0x4+0x2+1x1
   => 128+0+0+16+0+0+0+1
   => 145
in decimal it is 145
so, exponent/bias is 145-127 = 18
frac bits are 0000000000100000000001

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.0000000000100000000001 * 2^18
1.0000000000100000000001 in decimal is 1.000488519668579
   => 1.0000000000100000000001
   => 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+0x2^-14+0x2^-15+0x2^-16+0x2^-17+0x2^-18+0x2^-19+0x2^-20+0x2^-21+1x2^-22
   => 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+0x6.103515625e-05+0x3.0517578125e-05+0x1.52587890625e-05+0x7.62939453125e-06+0x3.814697265625e-06+0x1.9073486328125e-06+0x9.5367431640625e-07+0x4.76837158203125e-07+1x2.384185791015625e-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+0.0+0.0+0.0+0.0+0.0+0.0+0.0+0.0+2.384185791015625e-07
   => 1.000488519668579
so, 1.000488519668579 * 2^18 in decimal is 262272.0625
so, 01001000100000000001000000000010 in IEEE-754 single precision format is 262272.0625
Answer: 262272.0625

venereology answered 7 months ago

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