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.

The standard parts are the 74138 (3-to-8), 74139 (dual 2-to-4), and 74154 (4-to-16), usually with active-low outputs and one or more enable inputs.

Where It’s Used#

The classic job is address decoding: the high bits of an address bus feed a decoder whose outputs are the chip-select lines, so each memory or peripheral responds only to its own address range. Decoders also drive one-of-many selection generally — enabling one device, lighting one indicator, decoding a sequencer’s step into a control line — and display drivers (BCD-to-seven-segment) are decoders with a custom output pattern. The 74138 is squarely in the “still used today” column: turning a binary selection into individual enables is a job a processor rarely absorbs cleanly.

The Same Chip as a Demultiplexer#

A decoder’s enable input is the key to a second identity. Feed data into the enable and the decoder becomes a demultiplexer — the addressed output follows the data while the rest stay idle. Decoder and demux are not two circuits but one, used two ways. The reverse operation — collapsing a one-hot input back to a binary code — is the encoder.