Hi Warren,

> Assume that you can multiply two 8-bit values in hardware and get a
> 16-bit result (e.g. ROM lookup table). It's straightforward to use
> this to multiply two 16-bit values:
...
> But if the hardware can only provide the low eight bits of the 8-bit
> by 8-bit multiply, is it still possible to do a 16-bit by 16-bit
> multiply?

Yes.  Given hex 8-b numbers ab and cd, use your 8×8=8 hardware multiply
to work out

    b × d = BD
    a × d = AD
    b × c = BC
    a × c = AC

and then shift and add:

    BD + (AD << 4) + (BC << 4) + (AC << 8)

> ** Back story. I'm designing an 8-bit TTL CPU which has 8-bit
> multiply, divide and modulo in a ROM table. I'd like to write
> subroutines to do 16-bit and 32-bit integer maths.

That's quite an unusual mix.  Eight-bit CPUs I can think of either have
no hardware multiply of which to take advantage,
e.g. http://6502org.wikidot.com/software-math-intmul, or have a 8×8=16.

-- 
Cheers, Ralph.