Half Adder

combinatorial-logic

Definition

Half Adder

A half adder is a 1-bit adder that takes in two inputs $A,B$ and produces a carry bit $C_{out}$ and the result $S$. The carry bit $C_{out}$ is the overflow bit and the result bit $S$ is the bit addition.

$A$	$B$	$C_{out}$	$S$
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

We can observe that $C_{out}$ is the XOR and $S$ the conjunction of $A$ and $B$:

$$\begin{array}{rl}{C}_{out}& =A\oplus B\\ S& =A\wedge B\end{array}$$