Help Understanding 8bit Floating Point Conversions with Decimals and Binary

I'm in a basic Engineering class and we're going through binary conversions. I can figure out the base 10 to binary or开发者_如何学编程 hex conversions really well, however the 8bit floating point conversions are kicking my ass and I can't find anything online that breaks it down in a n00b level and shows the steps? Wondering if any gurus have found anything online that would be helpful for this situation.

I have questions like 00101010(8bfp) = what number in base 10

Whenever I want to remember how floating point works, I refer back to the wikipedia page on 32 bit floats. I think it lays out the concepts pretty well.

http://en.wikipedia.org/wiki/Single_precision_floating-point_format

Note that wikipedia doesn't know what 8 bit floats are, I think your professor may have invented them ;)

Binary floating point formats are usually broken down into 3 fields: Sign bit, exponent and mantissa. The sign bit is simply set to 1 if the entire number should be negative, and 0 if the number is positive. The exponent is usually an unsigned int with an offset, where 2 to the 0'th power (1) is in the middle of the range. It's simpler in hardware and software to compare sizes this way. The mantissa works similarly to the mantissa in regular scientific notation, with the following caveat: The most significant bit is hidden. This is due to the requirement of normalizing scientific notation to have one significant digit above the decimal point. Remember when your math teacher in elementary school would whack your knuckles with a ruler for writing 35.648 x 10^6 or 0.35648 x 10^8 instead of the correct 3.5648 x 10^7? Since binary only has two states, this required digit above the decimal point is always one, and eliminating it allows another bit of accuracy at the low end of the mantissa.