Encoder

Also called: binary encoder, plain encoder, 4-to-2 encoder, 8-to-3 encoder, 2ⁿ-to-n encoder, non-priority encoder

A combinational circuit with 2ⁿ inputs and n outputs that outputs the binary index of its active input. The reverse of a decoder.

An encoder does the opposite of a decoder. It has 2ⁿ input lines and n outputs, and it reports which input is 1 as a binary number.

A plain encoder assumes its inputs are one hot: exactly one line is active. Then each output bit is a single OR gate. Write each input's index in binary and ask which indices set that bit. For a 4-to-2 encoder:

Y1 (weight 2) is 1 for inputs 2 and 3: Y1 = .
Y0 (weight 1) is 1 for inputs 1 and 3: Y0 = .

D0 doesn't appear at all, because index 0 is 00.

That simplicity has two blind spots:

Several active inputs. D1 and D2 together give 11, which wrongly claims D3.
No active input. Nothing active gives 00, exactly the same as "D0 is active".

The priority encoder fixes both: it reports the highest-priority active input, and adds a valid bit V that says whether any input is active at all.

Where it shows up: turning a row of buttons, sensors or interrupt lines into a compact binary code.

Worked examples

Example

An 8-to-3 encoder

Only input D6 is active. Find Y2 Y1 Y0, and the equations.

1.
6 = 110, so the output is Y2 Y1 Y0 = 110.
2.
Equations: Y2 = (indices with a 4 in them), Y1 = , Y0 = .
3.
Check: with only D6 = 1, Y2 = 1, Y1 = 1, Y0 = 0. ✓

Example

Breaking a plain encoder

Feed the 4-to-2 encoder D3 D2 D1 D0 = 0110 (two inputs active).

1.
Y1 = = 1 + 0 = 1.
2.
Y0 = = 1 + 0 = 1.
3.
Output 11 names D3, which isn't even active. The OR gates mixed the codes of D2 (10) and D1 (01).
4.
This is why real inputs usually go to a priority encoder.

Common mistakes

Giving an encoder more outputs than inputs. It's the other way round: 2ⁿ inputs, n outputs.
Trusting a plain encoder with several active inputs. Its output is the OR of their codes, which is usually wrong.
Forgetting that "D0 active" and "nothing active" look identical (00) on a plain encoder.

Practice Encoder

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Encoder is taught in Combinational Logic.

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