expanding multipliers, problem

Apr 26, 2006 4 Replies
R

Hello all,



I am attempting to expand the 18x18 multipliers as provided in the xilinx Spartan 3 series. I followed the proposed implemention of expanding the multipliers as described in the xapp467.pdf app note (figure 5). However, I arrived at an impasse: When the operand is splitted up in 2 or more partial operands of 18 bits, the sign-extension of the operand does not carry over -I'll expalin: E.g Lets say we want to multiply (-1)in18bitsx(1)in 22bits.The 22 bit operand is splitted in 2 4-bit(lsb) and 18-bit(msb) operands. Thus, when we multiply the lsb part: 3FFFFh(=-1)x1h=3FFFFFh(=-1), we obtain a non-nil answer. However, when we multiply the msb part:



3FFFFh(=-1)x00000h=000000000h, we obtain a nil answer. When the 2 partial products are added and the bits properly weighed as to constructed the final product, the msb bit(sign bit) will be 0. Consequently, resulting in a positive product when a negative one was expected (-1 was expected, FFFFFFFFFFh.)

I feel I must be doing something wrong.. Please advise



-Roger



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R

Ooops, I forgot to sign-extend the lsb partial product before the summing of the partial products. I hope that take care of the problem..

-Roger

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J

Are you performing the LSbit multiply as unsigned? Figure 5 of that app note shows the LSbits of the 22-bit A vector coming in unsigned while B is applied as defined.

A=M+L (L>0, M==A>>n) A*B = M*B + L*B

If B is negative, the L*B result is negative and the sign extension has to be included in the post-multiply adder.

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R

The lower parts of the inputs have to be treated as unsigned, and you need to form partial products of all the peices:

A = AH*2^n + AL B = BH*2^m + BL

A*B = AH*BH*2^(m+n) + AH*BL*2^n + AL*BH*2^m + AL*BL

AL and BL are unsigned, AH and BH are signed if A and B are signed.

In your case, I guess you have only one of the operands split so: A*B = AH*B*2^n + AL*B, AL is unsigned, AH and B are signed.

Your example has AH=0, AL=1, n=4, B=-1 A*B = 0 + -1 = -1. Keep in mind your partial products require sign extension to the full width of the full product in order to add them together.

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R

Sign extending the lower partial products fixed the problem. Now, the products obtained make sense.

Thanks

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