# Encoder
**A circuit that converts $2^n$ inputs to $n$ coded outputs.**
An **encoder** is a circuit which accepts a set of $2^{n}$ input lines and generates an encoded output to $n$ lines. Typically, an encoder refers specifically to a simple encoder in contrast to a priority encoder.
An encoder is the [[Duality#Electrical circuits|dual circuit]] of a [[decoder]].
## 1-of-$n
amp;nbsp;encoder
*$1$-of-$n$ encoders* or *simple* encoders can only accept *one* HIGH input at any time. The most common encoders of this type are $2^n$-to-$n$ encoders.
### $n$ power of 2-to-$n$ encoder
$2^n$-to-$n$-line encoders can be thought of as a circuit that encodes a decimal number, represented by a unique input line, and outputting its binary equivalent.
> [!Example] $4$-to-$2$ line encoder
> $A_{0}=D_{1}D_{2}\qquad A_{1}=D_{2}D_{3}$
>
> | $D_{3}$ | $D_2$ | $D_1$ | $D_0$ | |$A_1$ | $A_0$ |
> |:-------:|:-----:|:-----:|:-----:|-|:-----:|:-----:|
> | $0$ | $0$ | $0$ | $1$ || $0$ | $0$ |
> | $0$ | $0$ | $1$ | $0$ || $0$ | $1$ |
> | $0$ | $1$ | $0$ | $0$ || $1$ | $0$ |
> | $1$ | $0$ | $0$ | $0$ || $1$ | $1$ |
>
> ![[4to2Encoder.svg|450]]
## Priority encoder
A priority encoder only outputs according to the *most significant* input that is $1$. Thus, priority encoders can accept *more than one* HIGH input at a time.
Priority encoders also have an additional output called the *valid* output, which distinguishes between when all inputs are off and when $D_0$ is off.
Below is a $4$-to-$2$ priority encoder.
$A_{0}=D_{1}\bar{D_{2}}+D_{3}\qquad A_{1}=D_{2}+D_{3}\qquad V=D_{0}+D_{1}+D_{2}+D_{3}$
| $D_{3}$ | $D_2$ | $D_1$ | $D_0$ | | $A_1$ | $A_0$ | | $V$ |
|:-------:|:--------:|:--------:|:--------:| --- |:--------:|:--------:| --- |:---:|
| $0$ | $0$ | $0$ | $0$ | | $\times$ | $\times$ | | $0$ |
| $0$ | $0$ | $0$ | $1$ | | $0$ | $0$ | | $1$ |
| $0$ | $0$ | $1$ | $\times$ | | $0$ | $1$ | | $1$ |
| $0$ | $1$ | $\times$ | $\times$ | | $1$ | $0$ | | $1$ |
| $1$ | $\times$ | $\times$ | $\times$ | | $1$ | $1$ | | $1$ |
![[4to2PriorityEncoder.svg]]