[Math] IEEE-754 Format Conversion

arithmeticbinaryfloating point

Represent $11.0011*2^{10}$ using the
IEEE-$754$ standard for $32$-bit floating point
representation.

$0$-Sign Bit
$10001010-$Exponent
$1001100000000000000000$-Mantissa

Is this answer is correct ? I am bit confused .. Please Help

Best Answer

Your answer is almost correct, you only missed a $0$ in the mantissa. Your number is $1.10011_2\times 2^{11}=3264_{10}$. The sign bit is $0$ the biased exponent is $11+127=138= 10001010_2$ and the mantissa without the implied leading bit is $10011000000000000000000_2$. Concatenated this gives $$11.0011_2\times 2^{10} \rightarrow01000101010011000000000000000000_2\\ = 0100\_0101\_0100\_1100\_0000\_0000\_0000\_0000_2 =454C0000_{16}$$ Check it e.g. with http://babbage.cs.qc.cuny.edu/IEEE-754.old/Decimal.html

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