Hardware building blocks

01

Decoder

An n-to-2ⁿ decoder maps a binary code to one-hot output. For 2-to-4: Q0=I̅1I̅0, Q1=I̅1I0, Q2=I1I̅0, Q3=I1I0.

Build it yourself: 2-to-4 decoder · 1-to-2 decoder

02

Encoder

An encoder maps one-hot input to binary code. A basic encoder assumes one active input; a priority encoder chooses a winner if several are active.

Build it yourself: 4-to-2 encoder

03

Multiplexer

A MUX selects one data input. For 2-to-1: Q=S̅I0+SI1. In an ALU a MUX selects an operation result; in a datapath it selects a data source.

Build it yourself: 2-to-1 multiplexer · 4-to-1 multiplexer

04

Demultiplexer

A DEMUX routes one data input to a selected output. It resembles a decoder but has a separate data input that enables the selected line.

Build it yourself: 1-to-2 demultiplexer · 1-to-4 demultiplexer

05

How to distinguish circuits

Many-to-one is a MUX; one-to-many is a DEMUX; binary-to-one-hot is a decoder; one-hot-to-binary is an encoder. Count data and select lines before inspecting gates.

06

Practical uses

A decoder selects a memory word/device, an encoder compresses requests, a MUX builds datapaths and selects ALU output, and a DEMUX distributes a stream across channels.