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omara007
Joined: 06 Jan 2003
Posts: 1279
Helped: 39
Location: Dubai
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 02 Nov 2009 1:28 How to multiply 2 signed Fixed-Point numbers ? |
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Hi guys
I have two 16-bit bit vectors .. each one represents a signed binary number. The format of each vector is as follows:
XXXX . XXXXXXXXXXXX
Where the (dot) represents the binary point that separates the integer part from the fraction part.
The Most Significant Bit order is (15), while the Least Significant Bit order is (0).
As the vector is signed, bits (12, 13, 14) represent the integer value while bit (15) is the sign bit. The numbers are represented in 2's complement format.
Now, I want to multiply these 2 vectors. I know that the result will be placed in a 32-bit vector. Yet, where will be the position of the binary point ? .. Please notice that it's a signed multiplication process.
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GeorgeM
Joined: 19 Nov 2003
Posts: 37
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02 Nov 2009 13:05 Re: How to multiply 2 signed Fixed-Point numbers ? |
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| The fraction part is 12+12=24 bit long. Doesn't matter either it signed or not.
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FvM
Joined: 22 Jan 2008
Posts: 5154
Helped: 766
Location: Bochum, Germany
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02 Nov 2009 20:10 How to multiply 2 signed Fixed-Point numbers ? |
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| Yes, so you have to drop 12 fractional bits and use saturation logic for the integer part.
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omara007
Joined: 06 Jan 2003
Posts: 1279
Helped: 39
Location: Dubai
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03 Nov 2009 22:07 Re: How to multiply 2 signed Fixed-Point numbers ? |
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| FvM wrote: |
| Yes, so you have to drop 12 fractional bits and use saturation logic for the integer part. |
Didn't understand what you said exactly .. please elaborate more ..
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GeorgeM
Joined: 19 Nov 2003
Posts: 37
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04 Nov 2009 12:53 Re: How to multiply 2 signed Fixed-Point numbers ? |
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| You were told in plain english: the product fraction size will be 24 bit. That is (4.12) x (4.12) = (8.24).
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FvM
Joined: 22 Jan 2008
Posts: 5154
Helped: 766
Location: Bochum, Germany
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04 Nov 2009 13:30 How to multiply 2 signed Fixed-Point numbers ? |
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Drop (or cut) 12 fractional bits is self-explanatory, I think. If you have doubts about needing saturation logic, you may want
to play around with numeric examples and consider, how you intend to handle a numeric overflow.
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omara007
Joined: 06 Jan 2003
Posts: 1279
Helped: 39
Location: Dubai
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05 Nov 2009 12:00 Re: How to multiply 2 signed Fixed-Point numbers ? |
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| GeorgeM wrote: |
| You were told in plain english: the product fraction size will be 24 bit. That is (4.12) x (4.12) = (8.24). |
Thanks GeorgeM .. Yet, I don't think my last comment was intended for you .. did you notice that I quoted FvM ?
| FvM wrote: |
Drop (or cut) 12 fractional bits is self-explanatory, I think. If you have doubts about needing saturation logic, you may want
to play around with numeric examples and consider, how you intend to handle a numeric overflow. |
Yes FvM .. it's about Saturation Logic .. did you assume I won't use a 32bit register for the output ?
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