Re: Decimal carry-save adder using reversed biquinary notation

On Tue, 13 Jun 2006 22:29:10 +0200, Terje Mathisen
<terje.mathisen@xxxxxxxxxxxxx> wrote, in part:

I did state that all those adders should work in carry-save format, in
fact that was an explicit requirement to be able to get the initial
mul_by_2 for free.

I.e. all 8 or 9 add stages except for the last would be 'fast', which
seems similar to what you're suggesting?

It's not clear to me where you're getting the multiples from without
carrying; I did work out a way, using bi-quinary/qui-binary conversion
to double (and quintuple) a decimal number without carries...

ah, you're converting to carry save format, which means you have two
inputs instead of one... but that doesn't work for decimal carry save,
because the second item is only a set of carries, not a full decimal
number.

Still, if you supply two inputs, rather than one input, for each
multiple, you have just added one layer to the Wallace tree, and the
starting point to improve on is having to supply *nine* inputs for each
multiple. I had to use a multiplication table to go down to two inputs.

Since the following multiples are obtainable through
bi-quinary/qui-binary conversions and shifts:

1, 2, 4, 5, and 8

can any other multiple be made up of a sum of two of them?

Why, yes. 3 = 1+2, 6 = 4+2, 7 = 5+2, and 9 = 8+1 or 4+5.

Was this what you were proposing? But you didn't mention the trick I
used to get 2x and 5x for free, so it must be something else.

John Savard
http://www.quadibloc.com/index.html
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