Binary representation of stored integer of fi object

2013 3 18
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I am using a lookup table with values ranging from 0 to pi/4.
These values are all less than one, i.e. 0 to .7854.
I am using the bin function to get the eight MSBs of a 16 bit number.
I noticed that bin(fi(.5000,0,16)) = 1000 0000 0000 0000 but bin(fi(.4555, 0, 16)) = 1110 1001 0011 0111
with bin(fi(.2500,0,16)) = 1000 0000 0000 0000.
Why do .5 and .25 have the same binary representation? Why does .4555 have a larger sized binary representation?

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Titus Edelhofer
Titus Edelhofer 2013-3-18

0 个投票

Hi,
if you only specify the word length and not the fraction length you get two different objects:
>> fi(0.25, 0, 16)
ans =
0.2500
DataTypeMode: Fixed-point: binary point scaling
Signedness: Unsigned
WordLength: 16
FractionLength: 17
>> fi(0.5, 0, 16)
ans =
0.5000
DataTypeMode: Fixed-point: binary point scaling
Signedness: Unsigned
WordLength: 16
FractionLength: 16
Note the difference on the FractionLength.
Now if you want to have numbers between 0 and 1, so FractionLength 16, you get what I think you are looking for:
>> bin(fi(0.5, 0, 16, 16))
ans =
1000000000000000
>> bin(fi(0.25, 0, 16, 16))
ans =
0100000000000000
Titus

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