Scale decimal number in FPGA

[gary36]

Hi

I have simple subsystem consisting of 4 digit pushwheel switches, FPGA and a 16 bit DAC. DAC maximum output is 5V corresponding to 65535 counts.
When I set 5000 through push wheel switches, the output of DAC must read 5.000V. To do this I have to use FPGA and not a microcontroller. FPGA must convert BDC digits 5000 (20480-decimal) to 65535 for proper display. Please provide the method to do so.

 

[barry]

How is 5000 = 20480 decimal? 5000 decimal is, um, 5000. For some reason, you are assuming 5000 BCD is 5000 hex.

Compute 65535/5000=13.107. That's your scale factor.

Simply take the value read from the switches and multiply by 13.107 to get the value you send to the DAC.

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I suppose you could read the switches as hex nybbles. In that case, your scale factor would be 65535/20480=3.2

 

[ads-ee]

Compute 65535/5000=13.107. That's your scale factor.

To implement this in an FPGA the values should be converted to fixed point binary first. You would convert the BCD input into a binary value and multiply it by the fixed point binary scale factor.

I suppose you could read the switches as hex nybbles. In that case, your scale factor would be 65535/20480=3.2

Using input BCD value as hex nybbles results in different scale factors every time the count rolls over between 9d to 0d instead of Fh - 0h.

e.g. 4999d * 13.107 = 65521.893
but 4999h = 18841d * 3.2 = 60291.2

 

[gary36]

Hi Barry,
How do I scale value by 3.2 in FPGA? Anyhow I came up with the following roundabout solution

1. Convert BCD 5000 to binary 5000
2. Scaling factor is now 65535/5000= 13.107. So I multiply 5000 * 1307 = 65535000
3. Convert 65535000 to BCD and then knock off the last 12 digits to get back 65535.

Do you have simpler solution than this one?

 

[andre_luis]

Scaling factor is now 65535/5000= 13.107. So I multiply 5000 * 1307 = 65535000

Didn't you note your above logic returns the original value 65535 = ((65535/5000)*5000) ?
Didn't you note you missed one digit "1" along the above step ?
Didn't you note you missed the decimal point ?

How do I scale value by 3.2 in FPGA?

Whenever you scale a float point value with a platform which do not provide native support for float point opperations, consider using the multiply-shift approach, which has the drawback of adding an intrinsic error, so it should be checked if meets your accuracy requirement, for example ( in pseudo-code ) :

Output =  3.2 * input =
Output =  ( 256 / 256 ) * 3.2 * input =
Output =  ( ( 256 * 3,2 ) / 256 ) * input =
Output =  ( ( 819,2 ) / 256 ) * input

However, since we should use only integers, 819,2 should be replaced by 819, adding an overal math error of 0,02% (=(819,2-819)/819,2)), pretty acceptable IMO for most applications.

Output =  ( ( 819 * input ) >> 8 )

 

[gary36]

Hi Andre

Your proposed method does not work for other values. For example BCD value of 2500 corresponds to 9472 in decimal. Now 9472*819/256 yields 30303. DAC output is 2.311 volts . This is a huge error.

 

[andre_luis]

You completely missed the point, review step-by-step the proposed method and the quoted question for what it refers to.
The key point on this approach is the replacement of a division opperation by a shift-right opperation.
BTW, according to your last reasoning, the scale factor is being used twice: 30303 = 2500 * 3.2 * 819/256.

Keep in mind that power-of-two numers at the denominator (Y/2ⁿ), return the same value that a right-shift (Y>>n) would do.

 

[gary36]

Hi andre

Please tolerate my ignorance. Here are my calculations

BCD-5000, Decimal 20480 , out= (20480*819)>>8 = 65520 = 4.9998 from DAC

BCD - 2500, Decimal 9472, out =(9472*819)>>8= 30303 = 2.311 from DAC

Could you please correct me if anything is wrong with the calculations. I am not considering scaling factor twice

 

[KlausST]

Hi,

Your mistake lies in BCD to decimal conversion: (edit: corrected values)
"BCD" value of "5000" = 0101 0000 0000 0000 (bin) should be formed into 5000 decimal = 1388 (hex) = 0001 0011 1000 1000 (bin)

"BCD" value of "2500" = 0010 0101 0000 0000 (bin) should be formed into 2500 decimal = 09C4 (hex) = 0000 1001 1100 0100 (bin)

BCD is already a "decimal" representation, thus it already looks identical: "1234" BCD = 1234 decimal.
But binary (hex) representations look different.

Klaus

 

[gary36]

Resolved. Thanks and its working now.