adding lec10 half adder

cst337/lec/lec10.md

@@ -1,4 +1,32 @@
 # lec10
 
-> whole section still needs to be transcribed over fom paper
+## Half-adder
+
+This will be the building block for adding bit-strings together later on however, for now we are going to just add two singular bits.
+To accomplish this we'll build a half adder.
+
+This means our logic circuit must adhere to the following logic table.
+If both inputs are 0 then our result is 0 and we don't have to carry anything out.
+If only one input A/B is 1 then our result will clearly be 1 and our carry will be 0. 
+Finally if both inputs are 0 then since we can't fit 2 in a single bit it means we have to carry-out a 1, and our result will be 0.
+
+With all of this in mind we have a table to guide how we will implement our logic circuit.
+I __highly__ suggest that you try to build a logic circuit on your own first as most of the content is best learned through practice.
+
+| A | B | Carry-out | Result |
+|---|---|---|---|
+| 0 | 0 | 0 | 0 |
+| 0 | 1 | 0 | 1 |
+| 1 | 0 | 0 | 1 |
+| 1 | 1 | 1 | 0 |
+
+![fig0](../img/fig0lec10.png)
+
+## Full Adder
+
+If we only want to add single-bit's then a half-adder works fine but if we want to add multiple bits say `1011 + 0010` then we need to consider that we will likely have to chain these together.
+The full-adder has 1 main difference from the half-adder, it has 3 inputs, 2 main inputs and 1 input for the carry bit.
+The carry bit will propagate along the operation now if we chain these together, _just like real addition_!
+
+![fig1](../img/fig1lec10.png)