Question

I am trying to decipher some assembly code that involves multiple left rotations on an 8-bit binary number.

For reference, the code is:

lab:    rol    dl,1
        rol    dl,1
        dec    ecx
        jnz    lab

The dec and jnz isn’t an issue, but is there to show that the 2 rols are executed several times.

What I am trying to do is figure out a mathematical equivalent of this code, such as a formula. I’m certainly not looking for a complete formula to tell me the whole code, but I would like to know if there is a formula that gives the equivalent (in denary) of a single left rotation.

I’ve tried figuring this out with a couple of different numbers, but cannot see a link between the two results. For example: if the start number is 115 it comes out as 220, but if the start number is 99 it comes out as 216.

Answer 1

Given your sample results, I assume we are treating the 8-bit quantity as unsigned.

The 7 low-order bits are shifted left, multiplying that part of the number by 2; and the high-order bit is swapped around to the beginning.

Thus, (x % 128) * 2 + (x / 128), using the usual integer div/mod operators.