Selection on Digital Logic Notebook

Decoder

Mon, 01 Jan 0001 00:00:00 +0000

Decoder#

A decoder takes an n-bit binary code and activates exactly one of its 2ⁿ outputs — the one whose number matches the input. A 3-bit input picks one of eight outputs, a 4-bit input one of sixteen. It turns a compact binary number into a one-hot signal: “this specific one, and no other.”

Every Output Is a Minterm#

Internally, each output is an AND of the input bits in a particular true/complemented combination — output 5 of a 3-to-8 decoder is high only for the input 101. That combination is a minterm, so a decoder generates all the minterms of its inputs at once. Because any Boolean function is a sum of the minterms where it is true (its sum-of-products form), a decoder plus a single OR gate can build any function of its input variables — which is one reason decoders show up far beyond their obvious use.

Encoder

Mon, 01 Jan 0001 00:00:00 +0000

Encoder#

An encoder is the reverse of a decoder: it takes 2ⁿ inputs, one of them active, and produces the n-bit binary code that names which one. Eight input lines become a 3-bit number, sixteen become a 4-bit number. Where a decoder expands a code into one-hot, an encoder compresses one-hot back into a code.

The Problem of More Than One#

A plain encoder assumes exactly one input is active. If two are high at once, the naïve output is meaningless — it is neither input’s code. Real inputs do not cooperate, so the useful part is the priority encoder: when several inputs are active, it outputs the code of the highest-priority one and ignores the rest, usually flagging separately whether any input was active at all. The standard parts are the 74148 (8-to-3 priority) and 74147 (10-line-to-4-line BCD priority).

Multiplexer

Mon, 01 Jan 0001 00:00:00 +0000

Multiplexer#

A multiplexer (mux) selects one of many inputs and passes it to a single output, chosen by a set of select lines. With n select lines it picks among 2ⁿ inputs — an 8-to-1 mux needs three. It is the fundamental data router: many sources, one destination, and a control that decides which source gets through.

The standard parts are the 74151 (8-to-1), 74153 (dual 4-to-1), and 74157 (quad 2-to-1). Internally a mux is a decoder on the select lines enabling one input path, all OR-ed together — select, gate, combine.

Demultiplexer

Mon, 01 Jan 0001 00:00:00 +0000

Demultiplexer#

A demultiplexer (demux) is the reverse of a multiplexer: it takes a single input and routes it to one of many outputs, chosen by the select lines. One source, many destinations, and a control that decides which destination receives the signal while the others stay idle.

The Same Hardware as a Decoder#

A demux is not a distinct circuit — it is a decoder with its enable input used as the data input. The decoder already activates exactly the one output named by the select lines; feed data into its enable and that selected output follows the data instead of simply going active. This is why a part like the 74138 is sold as a “decoder/demultiplexer”: the two functions are one piece of silicon addressed two ways. When the input is held permanently active it is a decoder; when the input carries data it is a demux.