Let's start with the basics. Ad John says, if when you say FA you mean a full adder, this is a logical function that adds two binary bits (a and b) -- it also adds a carry-in (ci) bit -- and it generates a sum (s) output bit and a carry-out (co) output bit as illustrated below.
The interesting line in the truth table is when a and b and ci are all 1. In thsi case we have 1 + 1 + 1 = 11 in binary or 3 in decimal.Now let's say we want to add two 8-bit binary numbers together. Let's call these a[7:0] and b[7:0], which means they each have 8 bits numbered from 7 (the most-significant) down to 0 (the least significant). We might also call these bits a7, a6, a5, a4.... etc.What we can do is take eight of out full adders shown above and connect them together to form an 8-bit binary adder as illustrated below:
So, in the case of your example where 5 + 4 = 9 in decimal. If we are dealing with 8-bit quantities, then 5 = 00000101 (let's call this our a[7:0] value) and 4 = 00000100 (let's say this is our b[7:0 value). Let's suppose we feed these two binary values into our binary adder shown above, in this case the result will be as shown below:
So 00000101 + 00000100 = 00001001 in binary, which is exactly the same as 5 + 4 = 9 in decimal. The point of all this is that it doesn't matter what number system you are working in, the underlying operations and results are all the same.
