# IEEE-754 Format Conversion

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

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

• @HimanshuChawla If $11.0011$ really mean a number in base $2$ (It is not clear in your question), then gammatester answer is the one you want. – achille hui May 29 '15 at 11:09
• But if $11.0011$ is in binary, who is to say what the exponent $10$ means? – TonyK Dec 8 '16 at 13:29
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