How can increase the precision in matlab to 24 bits after the decimal point?

Hi, I want to write a code to produce the 24 bits after the decimal point, but I can't found any instruction in matlab for it. Please help me.

Thanks

Answer 1

[Vahid]

Dear Walter I think I can use vpa to use the 24 bits after the decimal point. same as this number: 1.4016050745784331201804207012174

Thank you,

Vahid

[Walter Roberson]

No, vpa allows you to select the number of significant decimal digits, *total*, including the ones before the decimal point. There is no way with vpa to ask for a particular number of decimal digits after the decimal point.

For example, if you were currently working with 3 digits in vpa, then 0.123 * 10 would be 1.23 (3 total significant digits) and would _not_ be 1.230 (3 digits after the decimal point)

Reminder: 24 *bits* after the decimal point would mean that no matter how large your number was (say, 484539 before the decimal point) that you wanted the resolution after the decimal point to be 1 part in 2^24 (24 *bits*), which is 1 part in 16777216 which is just slightly better than about 6E-8

[Vahid]

Dear Walter

You are right.I want to show a number with 24 bits and then separate 16 bits from these 24 bits.For example this number:0.4999

I thought the vpa can help me to achieve this goal.

Could you help me?

Thanks

[Walter Roberson]

vpa() works with decimal, not with binary, so NO, vpa cannot be used for your purposes. Perhaps the Fixed Point Toolbox would be appropriate for you.

I am getting a definite impression that we have a terminology difference. A "bit" is, by definition, a Binary digIT, each a single position that can represent only the two values 0 or 1. VPA works with decimal places, which has to do with decimal digits, each a single position that can represent any of the 10 values, 0 1 2 3 4 5 6 7 8 9 .

Slightly more than 3 bits (binary digits) are required to represent each decimal digit. 16 bits of fraction would be able to represent 1 part in 65536, which would get down to about 1.5E-5

Answer 2

[Walter Roberson]

You need to use a software fixed-point system to work with any particular number of bits after the decimal point.

Please note that "bits" refers to numeric representation in base 2, but "decimal point" refers to numeric representation in base 10. Do you perhaps need a particular number of decimal digits after the decimal point? For example it would seem strange to work with values in the range of 10^200 and then expect 24 bits after those 200 decimal digits.

You might be able to use the Fixed Point Toolbox for your purpose, but note that not all routines support the Fixed Point Toolbox.

MATLAB uses IEEE 754 Double Precision, which has 53 bits of precision total, but that is floating point.

Possibly though all you need at this time is to look at the command

format long g