Internally truncated multiplier
A multiplier circuit includes a partial product generation circuit, a truncation circuit, and a summation circuit. The partial product generation circuit is configured to generate a plurality of partial products for multiplying two values. The truncation circuit is coupled to the partial product generation circuit. The truncation circuit is configured to shorten at least some of the partial products by removing a least significant bit from the at least some of the partial products. The summation circuit coupled to the truncation circuit. The summation circuit is configured to sum the truncated partial products produced by the truncation circuit.
1. A multiplier circuit, comprising:
a partial product generation circuit configured to generate a plurality of partial products for a multiplier and a multiplicand;
a truncation circuit coupled to the partial product generation circuit, the truncation circuit configured to shorten at least some partial products of the plurality of partial products, by removing a least significant bit from the at least some of the partial products, to generate truncated partial products;
a summation circuit coupled to the truncation circuit, the summation circuit configured to sum the truncated partial products, to generate a multiplication product; and
a bias compensation circuit coupled to the summation circuit, the bias compensation circuit configured to generate a bias compensation value based on whether the multiplier and the multiplicand are random.
2. The multiplier circuit of claim 1 , wherein the bias compensation circuit is further configured to:
determine a bias introduced by the truncation circuit; and
generate the bias compensation value based on the bias.
3. The multiplier circuit of claim 1 , wherein the summation circuit is further configured to add the bias compensation value to a sum of the truncated partial products.
4. The multiplier circuit of claim 1 , wherein the bias compensation circuit is configured to generate the bias compensation value based on a number of the partial products truncated by the truncation circuit.
5. The multiplier circuit of claim 4 , wherein the bias compensation circuit is configured to increment the bias compensation value for each of the partial products that is truncated by the truncation circuit.
6. The multiplier circuit of claim 1 , wherein the bias compensation circuit is configured to generate the bias compensation value as a constant value.
7. The multiplier circuit of claim 6 , wherein the bias compensation circuit is configured to generate the constant value in response to determining that the multiplier and the multiplicand are statistically random.
8. The multiplier circuit of claim 1 , wherein the bias compensation circuit is configured to compute the bias compensation value based on a number of nonzero bits of the multiplier.
9. The multiplier circuit of claim 8 , wherein the bias compensation circuit is configured to compute the bias compensation value to be half the number of nonzero bits of the multiplier.
10. A digital down converter (DDC), comprising:
a mixer configured to multiply samples of a radio frequency signal with samples of a down conversion frequency, to produce an intermediate frequency signal, the mixer comprising:
a multiplier to multiply the samples of the radio frequency signal with the samples of the down conversion frequency, the multiplier comprising:
a partial product generation circuit configured to generate a plurality of partial products for multiplying a sample of the radio frequency signal and a sample of the down conversion frequency;
a truncation circuit coupled to the partial product generation circuit, the truncation circuit configured to shorten at least some of the partial products by removing a least significant bit from the at least some of partial products, to generate truncated partial products;
a summation circuit coupled to the truncation circuit, the summation circuit configured to sum the truncated partial products produced by the truncation circuit, to generate a multiplication product; and
a bias compensation circuit coupled to the summation circuit, the bias compensation circuit configured to generate a bias compensation value based on whether the sample of the radio frequency signal and the sample of the down conversion frequency are random.
11. The DDC of claim 10 , wherein the bias compensation circuit is further configured to:
determine a bias introduced by the truncation circuit; and
generate the bias compensation value based on the bias.
12. The DDC of claim 10 , wherein the summation circuit is further configured to add the bias compensation value to a sum of the truncated partial products.
13. The DDC of claim 10 , wherein the bias compensation circuit is configured to generate the bias compensation value based on a number of the partial products truncated by the truncation circuit.
14. The DDC of claim 13 , wherein the bias compensation circuit is configured to increment the bias compensation value for each of the partial products that are truncated by the truncation circuit.
15. The DDC of claim 10 , wherein the bias compensation circuit is configured to generate the bias compensation value as a constant value.
16. The DDC of claim 15 , wherein the bias compensation circuit is configured to generate the constant value in response to determining that the samples of the radio frequency signal and the samples of the down conversion frequency are statistically random.
17. The DDC of claim 10 , wherein the bias compensation circuit is configured to generate the bias compensation value based on a number of non-zero least significant bits of either the samples of the radio frequency signal or the samples of the down conversion frequency.
18. A method for multiplication, the method comprising:
generating, by a partial product generation circuit, a plurality of partial products for a multiplier and a multiplicand;
shortening, by a truncation circuit, at least some partial products of the plurality of partial products by removing a least significant bit from the at least some of the partial products, to generate truncated partial products;
summing, by a summation circuit, the truncated partial products, to generate a multiplication product; and
generating, by a bias compensation circuit, a bias compensation value based on whether the multiplier and the multiplicand are random.
19. The method of claim 18 , further comprising adding, by the summation circuit, the bias compensation value to a sum of the truncated partial products.
20. The method of claim 18 , wherein generating the bias compensation value is performed based on a number of the partial products truncated by the truncation circuit.