Fixed point multiplication in ASM

[Neil Pate]

Almost totally unrelated to LabVIEW, and is not really just a question more of just a ramble.

I have dusted off a PIC microcontroller that I have had lying around in my drawer for years, and am attempting to stop old-age brain rot my making it do stuff, but purposely limiting myself to assembler.

So far I have the (12-bit) ADC working, and sending the upper 8 bits back to the PC over RS-232 as an ASCII character.

Now all I want to do is display the analogue voltage on the PC. Should be simple. I am using the 5V supply as the reference, so a 12-bit ADC has a step size of 1.22 mV. Conversion from 12-bit hex value to human readable value should be reasonably straightforward: scale the ADC value by 1.22 mV, convert to say 5 digit BCD and chuck out over the serial port one character at a time. I figure the first step is to implement a fixed point multiplication, keeping things simple I can have the ADC reading as <+,16,0> and the scaling factor as <+16, 3>.

 This is the bit that is making my brain hurt... I have done some reasearch and it turns out that fixed point multiplication does not really care about the format of the number, only the bit-width. So you can use exactly the same algorithm to scale <+16,0> and <+16,3>. Anybody know if this is correct?

Now, I know I can take all sorts of shortcuts to get the ADC value in human readable format, I have decided for the purpose of the exercise I really want to figure this out using fixed point maths (I have no actual application in mind other than curiosity).

 

[JKSH]

 

6 hours ago, Neil Pate said:

 This is the bit that is making my brain hurt... I have done some reasearch and it turns out that fixed point multiplication does not really care about the format of the number, only the bit-width. So you can use exactly the same algorithm to scale <+16,0> and <+16,3>. Anybody know if this is correct?

Correct

A few useful notes:

• Your 16-bit fixed point number is stored in memory exactly like a 16-bit integer*.
• Fixed point multiplication == Integer multiplication. The same algorithms apply to both.
• The algorithms for integer multiplication don't depend on the value of the number. By extension, they don't depend on the representation of the number either.
  • e.g. Multiplying by 2 is always equivalent to shifting the bits to the left (assuming no overflow)

(* LabVIEW actually pads fixed point numbers to 64 or 72 bits, but I digress)

 

Anyway, to illustrate:

 Bit Pattern (MSB first) | Representation                | Value (decimal) 
=========================|===============================|=================
 0000 0010               | <+,8,8> (or equivalently, U8) | 2
 0000 0010               | <+,8,7>                       | 1
 0000 0010               | <+,8,6>                       | 0.5
-------------------------|-------------------------------|-----------------
 0000 0100               | <+,8,8> (or equivalently, U8) | 4
 0000 0100               | <+,8,7>                       | 2
 0000 0100               | <+,8,6>                       | 1

 

 

6 hours ago, Neil Pate said:

  Almost totally unrelated to LabVIEW, and is not really just a question more of just a ramble.

That's borderline blasphemy...  You can redeem yourself by getting LabVIEW involved:

Edited September 6, 2016 by JKSH

[Neil Pate]

I did say "almost" :-)

This is the VI I knocked up just to test things out..

 

Thanks for the info, I will digest slowly tomorrow evening.

Edited September 6, 2016 by Neil Pate

[Neil Pate]

Getting there slowly.. :-)

I have the 16-bit x 16-bit multiplication working using the 8-bit hardware multiplier.

Also I have fleshed out my LabVIEW demo to show how to solve the rest of my problem.

 

Convert (+,16,4) Fixed Point Number To String.vi

Convert First Decimal Place Of (+,16,4) Fixed Point Number To String.vi

Fixed Point Maths.vi

Edited September 10, 2016 by Neil Pate