Experiment 11 - The Half Adder

To add two numbers is one of the standard functions of a computer. But how do you implement this with a digital circuit?

To solve this task, you have to bear in mind the logic of a binary addition...

0	0	1	1
+  0	+  1	+  0	+  1
= 00	= 01	= 01	= 10

Binary Addition.

If you are expecting only a 1-bit response, everything looks easy. All you need for this is a XOR XOR gate.

But if you are adding a 1 and 1, the answer is more complicated. A 1 must be transmitted to the next position. This bit is called the Carry bit. And as an output of a logic circuit, it is indicated by CO (Carry Out).

A B Q CO 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 Truth Table Half Adder.

Circuit Diagram Half Adder.

Circuit Half Adder. (Enlarge)

You realize the result for CO by using an AND gate, as you see from the truth table. The adder of two one-digit binary numbers is called a half adder. But what you need to add two 4-digit numbers?