decimal to IEEE floating-point

To convert a decimal number to IEEE floating-point representation:

1. Find binary representation $n$ of the decimal number.
2. Multiply $n$ by $2^0$ so that we now have $n\times 2^0$ (just like scientific notation, except the base is 2).
3. Try to put number in the form 1.m (m = mantissa; base-2 scientific notation) by increasing or decreasing the exponent field and moving the decimal (binary?) point accordingly.
4. The floating-point exponent field is the current exponent (on $2$) but plus 127. We need to do this since in IEEE representation, 2 is raised to the power of $\exp -127$.
5. Zero-pad the mantissa on the right if its length is fewer than 23 bits.
6. Set the sign bit to 1 if original number is negative.
7. Concatenate sign, exponent, and mantissa bits to get your floating-point representation of the decimal number.