Normalized Float Point

[Starquizer]

I was searching all over the internet and YouTube videos on how float are stored in computer memory as binary, I found out how but I was stuck at the part on how to normalize a binary number, some sites and videos say that it is in this format '0.1011 x 2^e' and others say you must have a leading 1 like this '1.0110 x 2^e' also according to many sites I read, it is the leading 1 that is normalized.

With 8-bit system:
1 bit for the sign
3 bit for the exponent
4 bit for the mantissa

I saw a video that represents 7.0

0

011

1110

and another site as

0

101

1100

Which is correct ?

 

[deathismyfriend]

Floats are stored several different ways. I think based on regions ? So both of those could be correct.

 

[Starquizer]

Floats are stored several different ways. I think based on regions ? So both of those could be correct.

Could be or could be not. All I know is that you can't represent 0.0 with normalized form; it must be denormalized, or at least that's what I have read.

 

[Geries]

Most widely supported float format is the IEEE 754 float, and you can find several information on wikipedia: http://en.wikipedia.org/wiki/IEEE_floating_point Minifloats. On the other hand there are lots of float formats to fit for other needs ie: speed, size, precision, etc.

 

[deathismyfriend]

Most widely supported float format is the IEEE 754 float, and you can find several information on wikipedia: http://en.wikipedia.org/wiki/IEEE_floating_point Minifloats. On the other hand there are lots of float formats to fit for other needs ie: speed, size, precision, etc.

Thanks for clearing that up and for the links. + Rep

 

[Starquizer]

Most widely supported float format is the IEEE 754 float, and you can find several information on wikipedia: http://en.wikipedia.org/wiki/IEEE_floating_point Minifloats. On the other hand there are lots of float formats to fit for other needs ie: speed, size, precision, etc.

I know about the wiki site but didn't read much because those equations were making me nuts (thanks anyway) and I guess that there is no modern computer storing a float on a 8-bit, it was just an academic question about normalization/denormalization.

~thx again~

 

[Dr Super Good]

'1.0110 x 2e'

Is the normalized form. You get rid of any leading 0s to normalize it. This may not reflect how the number is stored as due to normalization you always know the first bit is a 1 and so you do not need to store it (kind of compression).

8 bit floats are impractical to use as the range and granularity provided is small and the computation overhead is still high. Since the range makes them impractical it is unlikely to have hardware acceleration meaning slow software simulation. This means that it is undoubtedly faster to compute 64 bit fixed point which is likely a lot more useful. Since most powerful systems have 32bit and 64bit float hardware acceleration it is logical that these will be commonly used.