csnotes/337/lec/lec4.md

lec4

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.