On: MCS-48: The quest for 16-bit division on the 8-bit...

[phire]

Also, rearrange the calculation. (Celsius * 9) / 5 can trivially be rearranged to Celsius * (9 / 5)

You can implement this as a fixed point multiply by the constant 1.8.

You are already using base 10 fixed point, so it simply becomes a multiply by 18, which can be simplified to a few shifts and adds:

(Celsius << 4) + Celsius + Celsius

Don't forget to add 32 and the algorithm requires a 16bit shift and three 16 bit adds.

[SilasX → phire]

>Also, rearrange the calculation.

Yep, for the nand2tetris course, we had division, but it was in the OS, and a really expensive operation. I wrote a program that needed to know which third of a line a point was on. (i.e. identify 4 on a 15-length line as being in the first third).

I naively wanted to do something like "if x < L / 3", but rearranged it to "if x * 3 < L". (Of course, the language only supported integers and not fractions or floating point, so I needed to do that anyway.)

[bonzini → phire]

But then you are in base 100 fixed point. Converting it back to base 10 is what requires a division (but it's still by a constant though).

[phire → bonzini]

Op is already in base 100 fixed point. I guess because that's what the sensor returns?

Though it might be smart to convert it to another format. Four nibbles of BCD would be ideal and the MCS-48 looks to have native support for it.

Thought you would need a custom version of shift by 4 that handles BCD.

Or simplify the equation to just adds:

    C2 = C + C
    C4 = C2 + C2
    C8 = C4 + C4
    C16 = C8 + C8
    Res = C16 + C2

[bonzini → phire]

If he's in base 100 and you multiply by 18 it's the same story: you are now in base 1000 and need a division to go back.

Converting from binary to BCD also needs division by constants, so again it's more or less the same.

[phire → bonzini]

Oh, right. I'm an idiot who forgot about the fixed point divide.

And yes, at some point you are going to need to do a divide by constant 10. It's unavoidable if you want a base 10 display. The option of using BCD to do calculations just lets you do that divide upfront, rather than at the end.