Editing Basic Assembly Programming (section)

===== Complex Operations From Simple Ones (XOR) =====

We can break the XOR operation into smaller steps. Recall that the XOR of <code>a</code> and <code>b</code> is <code>a ^ b = (a | b) &amp; ~(a &amp; b)</code>. In words, the XOR of two bits is 1 if their OR is 1, ''and'' their AND is 0. We have OR and NAND operations, so we can do these things. We need to save some intermediate values while we’re working. We’ll use register 0 since it’s free. Notice how we shuffle data around into the correct registers as needed.

<pre>move|s4|d1  # the value we saved earlier
move|s3|d2  # the mask we just computed
or          # their bitwise OR
move|s3|d0  # save that so it isn't overwritten by...
nand        # their bitwise NAND
move|s0|d1  # prepare to operate on their OR...
move|s3|d2  # and their NAND...
and         # the result of the XOR.</pre>
Now we have the bitwise complement of the value that was in register 0. It’s in register 3, but from here we could move it wherever we want.

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