Experiment 12 - The Full Adder

How do you add two 2-bit numbers? You could write down the complete truth table, however this is complicated. More elegant is to find a partial solution for each digit of the binary number first.

Consider the second digit of the binary number. First the inputs A and B are added. Furthermore the transfered information from the first digit, the Carry Bit, has to be added. Hence the circuit gets a third input, the Carry-IN CI. Such a logical unit is called a full adder.

CI A B Q CO 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 Truth Table Full Adder

Circuit Diagram Full Adder.

There are many ways to build a full adder using logic gates. The circuit chosen here consists of two half adders with an additional OR gate.

Circuit Full Adder. (Enlarge)

Now back to the problem of two 2-bit numbers to be added.