Build a Decoder

CSC-116 · Semester I · Digital Logic

intermediate25 minAvailable

Live simulation12 components · 14 wires

OFF

NOT

Y01

Y10

Y20

Y30

Click a switch to toggle it · drag output → input to wire · drag to move · Delete removes the selection · Ctrl+Z undoes.

Truth table

live from the current circuit

A	B	Y0	Y1	Y2	Y3
0	0	1	0	0	0
0	1	0	1	0	0
1	0	0	0	1	0
1	1	0	0	0	1

Lab brief

Objective

Build a 2-to-4 decoder from gates and verify that exactly one output activates for each input combination.

Theory & concepts

A 2-to-4 decoder has two inputs A, B and four outputs Y0-Y3. Output Yi is high exactly when (B,A) equals the binary value i. Each output is one minterm of the inputs.

Rendering diagram…

2-to-4 decoder: one minterm per output

Y0 = B'A'    Y1 = B'A
Y2 = BA'     Y3 = BA

B A | Y3 Y2 Y1 Y0
0 0 |  0  0  0  1
0 1 |  0  0  1  0
1 0 |  0  1  0  0
1 1 |  1  0  0  0

Because each output is a minterm, a decoder plus one OR gate can implement any function: OR together the outputs for the rows where the function is 1. Adding an enable input gates every output off at once.

Prerequisites

Lesson: Logic gates and truth tables
Lesson: Decoders

Instructions

1Add two switches for inputs A and B.
2Add two NOT gates to produce A' and B'.
3Add four 2-input AND gates and wire each to one minterm (B'A', B'A, BA', BA).
4Connect each AND output to its own LED labelled Y0-Y3.
5Toggle all four input combinations and record which LED lights.

Tasks

One-hot check
Confirm that exactly one output is high for each input combination.
Enable version
Add an enable switch and describe how gating it into each AND changes the circuit.
Function from decoder
Use the decoder plus one OR gate to produce F = Y1 + Y3 (that is F = B'A + BA).

Self-check

Exactly one decoder output is active for each input combination.
The minterm wiring matches the decoder truth table.
The student can build a Boolean function with a decoder and OR gate.

Environment

gate palettewire connectionslive simulationtruth table check