Binary representation of stored integer of fi object

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?

Answer 1

[Titus Edelhofer]

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

Answer 2

[Charles Jackel]

Thank you! That helped a lot!