finding the range of floating point question..

[transgalactic]

a number of 36 bits with the representation of a floating point has 8 bits plus the sign bit for the exponent and 26 bits plus a sign bit for "mantissa"(what is that??)
the mantissa is normalized(whats normalized mantissa??)
the exponent and the mantissa numbers are represented by a sign bit
and the absolute value.

what is the biggest and the smallest number we can represent in this way excluding zero??


i read the articles on floating point
i understand that there is the integer part the mantissa part which is the fracture or all the letters before the point.

plus there is the exponent (10^x)which can move the point in our number.

i have trouble to image this number and how looks this exponent
how looks this whole thing
so i could see what its maximal range
???

 

[crutschow]

The mantissa contains the significant bits of the number.

Normalizing the mantissa means adjusting it so that its leftmost bit is nonzero.

The exponent determines the binary point location starting from the right of the left-most bit.

8-bits for the exponent would mean the maximum exponent value would be 255d.

26-bits for the mantissa means the mantissa would have a maximum value of 67108864d.

For example, the number Pi rounded to 24 bits is 11.001001000011111101101. In binary single-precision (24-bit) floating-point, this is represented as mantissa = 110010010000111111011011 with exponent = 1 (see Floating point - Wikipedia, the free encyclopedia)

 

[transgalactic]

??

so what is the greates number i can represent, using this notation?

 

[transgalactic]

i cant figure this out

i cant imagine the range of the numbers
the extreme numbers
on the ends


?????????

 

[crutschow]

so what is the greates number i can represent, using this notation?

In binary it would be 1.111111111111111111111111 with 230 zeros or approximately 57.9e75 in decimal.

 

[transgalactic]

ineed to find

the range

the smallest number and the biggest number

 

[Pommie]

The biggest positive number is
182,687,701,944,103,929,407,952,896,382,538,518,002,845,876,224.

That is 26 ones followed by 255 zeros converted to decimal.

The biggest number is,
-182,687,701,944,103,929,407,952,896,382,538,518,002,845,876,225.

This represents the above number negated and is bigger in magnitude.

Mike.
Edit, why is the BBS software inserting a random space in my numbers?

 

[Pommie]

I was wrong in the previous post. Crutschow was correct but I get 26 ones followed by 230 zeros to be,
22,300,744,866,223,624,195,306,750,046,696,596,435,894,272
Out by a factor of two but I don't know why and don't have time to investigate now.

Mike.

 

[Pommie]

Ignore my previous two post. I got the numbers completely wrong.

With the severly restricted edit facilities, there is going to be a lot of garbage posts like my two previous.

Mike.