The Full Adder

- The "staged adder" circuit is called a "Full Adder" circuit
The full adder

**adds 2 bits**together, along with a**carry in**from the previous bit-addition.The full adder generate a

**sum**bit and a**carry out**bit for theaddition stage.*next* - Thus, the full adder has 3 inputs:
- a, one of the bits to be added
- b, the other bit to be added
- c
_{in}, the carry in bit from the previous bit addition

and it has 2 outputs:

- s, the sum bit
- c
_{out}, the carry out bit for the next staged bit addition

Schematically:

The figure on the right shows the operation of the full adder circuit when it adds the bits 1 and 0, while the previous stage generates a carry (c

_{in}= 1). - We can design the full adder circuit using the technique
learn a couple of weeks ago (if you have forgotten it,
then: click here)
Here is the boolean function in table form for the adder circuit:

c _{in}a b c _{out}s - - - + - - 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 You can see that:

- c
_{out}= majority(a, b, c_{in}) - s = a XOR b XOR c

- c
- The adder circuit is a very common and important circuit and
electrical engineers have determine the
**optimal**digital circuit that implements the full adder.The optimal full adder circuit is as follows:

- Here is a logic-sim circuit file implementing a full adder:
click here

- To make a multi-bit adder, we concatenate or
**cascade**a number of full adder circuits.For example, the following circuit will implement a 4-bit adder circuit that can be used to add two 4-bit numbers:

- Here is a logic-sim circuit file implementing a 4-bit adder using
4 full adders:
click here
- To re-inforce the material learn, project 2 will now be assigned and ask you to design a multiply circuit using full adders: click here