# Digital Electronics - Full Adder

#### cheyenne

Joined Dec 6, 2007
48
I have a question asking me to design a logic circuit for a full adder using NAND gates.

I am finding it hard understanding this topic. Can someone explain to me how the outputs of the truth table are determined so I can understand this better.

#### Papabravo

Joined Feb 24, 2006
13,967
Well the outputs in the truth table follow the rules for binary addition. You use the same intuition that you have for decimal addition except you remember that you are in base 2 instead of base 10.
Rich (BB code):
0 + 0 = 0   in any number base
0 + 1 = 1   also true in any number base
1 + 0 = 1   addition is commutative
1 + 1 = 0   makes sense if you remembered to say "and carry the 1".
The Booleanly astute will recognize that the truth table for the binary sum is the same as the truth table for the exclusive-OR function. I leave the truth table for the carry bit as an exercise for the reader.