attempted long mult drawings REVD
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Short working document by Phil dated 6.16.13, recording a new attempt at drawings for multiplier circuits. It contains Figure 7, a polynomial multiplier circuit, and writes out the long multiplication of a degree-k polynomial h by a series in inverse powers of z with coefficients i. The k = 3 case is expanded row by row to give output coefficients o0 through o8. The drawings themselves are not in the extracted text.
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New attempt at drawings for multipliers PhL 6.16.13
Eventually I found a nice way to do these drawings.
Figure 7: A polynomial multiplier circuit.
hkzk + hk-1zk-1 + ...... + h2z2 + h1z + h0
irz-r + ir-1z-r+1 + .......................................................... + i2z-2 + i1 z-1 + i0
____________________________________________________________________
i0hkzk + i0hk-1zk-1 + i0hk-2zk-2............................ + i0h2z2 + i0h1z1 + i0h0z0
i1hk zk-1 + i1hk-1zk-2 + ........................................... + i1h2z1 + i1h1z0 + i1h0z-1
i2hk zk-2 + i2hk-1zk-3 + ..................................... + i2h2z0 + i2h1z-1 + i2h0z-2
xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k
xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k + xx-xyy-yzk-k
Figure 7 with k = 3:
h3z3 + h2z2 + h1z + h0
.... + i3z-3+ i2z-2 + i1 z-1 + i0z0
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i0h3z3 + i0h2z2 + i0h1z1 + i0h0z0
i1h3z2 + i1h2z1 + i1h1z0 + i1h0z-1
i2h3z1 + i2h2z0 + i2h1z-1 + i2h0z-2
i3h3z0 + i3h2z-1 + i3h1z-2 + i3h0z-3
i4h3z-1 + i4h2z-2 + i4h1z-3 + i4h0z-4
i5h3z-2 + i5h2z-3 + i5h1z-4 + i5h0z-5
**** + ***** + **** ...
***** + ****...
*****...
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o0z3 + o1z2 + o2z1 + o3z0 + o4z-1 + o5z-2 + o6z-3 + o7z-4 + o8z-5
= z3 [ o0z0 + o1z-1 + o2z-2 + o3z-3 + o4z-4 + o5z-5 + o6z-6 + o7z-7 + o8z-8