asm: lec 4 fixed

cst337/lec/lec4.md

@@ -1,9 +1,39 @@
 # lec4
 
-_this page to be updated late since i just got lazy this time_
-Topics to cover:
-* add/sub
-* intro to overflows
-* intro to carries
-* translating this to some 64 bit add/sub instructions and becoming more familiar with the flags register
-	* eflags won't be covered indepth yet but merely mentioned for sake of preparative clarity
+## Binary Addition
+
+Let's say we want to add the binary numbers `0b0011` and `0b1001`.
+
+To do this we have to consider what happens when we do `1+1`.
+If we only have 1 bit of space to work with then our answer is just `0`.
+In normal terms if we only have digit of space to work with 5+5 is also 0 but with a carry of 1.
+Same deal in binary: `1+1=0 {Carry=1}`.
+
+So now we have:
+
+```
+ 11  <-- Carry row
+0011 + 
+1001
+----
+1100 <-- Final answer
+```
+## Binary Subtraction
+
+Taking the problem `0011-1001` what we're actually going to do is find the 2's complement of the second number. 
+This will be the negative version of that number which means its equivalent to saying `0011+(-1001)`.
+
+So now we have basic addition but our `1001` becomes `0111`.
+
+```
+111  <-- carry bits
+0011 +
+0111
+----
+1010 <-- Final answer
+```
+
+Regardless of what happens we will always produce one special number alongside our result: _the carry bit_.
+This is just the bit that carries out from the computation.
+In both of our examples that bit would have been 0 but sometimes you'll notice that the carry is 1.
+Both scenarios are valid depending on what data your adding/subtracting.