# Half-Adder

#### Chapter 9 - Combinational Logic Functions

As a first example of useful combinational logic, let’s build a device that

can add two binary digits together. We can quickly calculate what the answers

should be:

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10_{2}

So we well need two inputs (a and b) and two outputs. The low order output

will be called Σ because it represents the sum, and the high order output

will be called C_{out} because it represents the carry

out.

The truth table is

Simplifying boolean equations or making some Karnaugh map will produce the

same circuit shown below, but start by looking at the results. The Σ

column is our familiar XOR gate, while the C_{out} column is

the AND gate. This device is called a half-adder for reasons that will make

sense in the next section.

or in ladder logic

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