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Altera_Forum
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14 years ago

Multiplication Rounding

Hey guys, I am multiplying two 32 bit numbers using LPM_MULT. Each number is in Q16.16 fixed point format. The product is a 64 bit Q32.32 number. I then shift the product to the ri...
Altera_Forum's avatar
Altera_Forum
Icon for Honored Contributor rankHonored Contributor
14 years ago

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Lets say you have Q2.2 notation. You have two numbers:

01.11=1.75

x 10.00=2.00

The product should be 3.50

If I do the binary multiplication in my calculator I get a Q4.4 result:

00111000

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So far, soo good.

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Now I perform the rounding by adding P(3) to P(7:4) I get:

0011+0001=0100

If I'm interpreting this correctly, it appears that my 3.5 rounded to a 4. But, there isn't any fractional part of the number. The rounding forced the result to Q4.0. Instead of getting 11.10=3.5, I got 0100=4.

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Your mistake is not in the rounding part, it's in the cutting part.

You had a Q4.4 value and trimmed it's 4 LSBs. Thus, you got a Q4.0 value. Q4.0 can only represent 3 or 4, not 3.5.

The rounding is actually correct for a conversion to Q4.0: it rounded 3.5 to 4.