DECODER Digital Logic Utility

Binary Decoder Circuit Simulator

Simulate binary decoder circuits including 2-to-4, 3-to-8 and 4-to-16 decoders. Set the binary input code, control the enable signal and see which one-hot output becomes active for the selected input combination.

✓ 2-to-4 Decoder ✓ 3-to-8 Decoder ✓ 4-to-16 Decoder ✓ Enable Input ✓ One-Hot Output ✓ Boolean Logic

DEC

Binary Decoder Simulation

● Ready

Binary Input Lines

Decoder Configuration

Decoder Size

Enable Input E

Output Logic

Decoder rule: An n-to-2ⁿ decoder activates exactly one output corresponding to the binary input value when enabled. For example, input 101₂ = 5 activates Y5 in a 3-to-8 decoder.

Decoder Result Output Active

Decoded Output —

Decoder —

Binary Input —

Decimal Input —

Enable E —

Active Output —

Outputs —

Logic Type —

One-Hot Valid —

Decoder Output Lines Active-high logic

2:4
DECODER

Decoder Logic Analysis —

Boolean Output Condition —

Binary Decoder Circuit Simulator

The Binary Decoder Circuit Simulator models standard combinational decoder circuits that convert an n-bit binary input into one of 2ⁿ output lines. Each possible binary input combination corresponds to one unique decoder output.

The simulator supports 2-to-4, 3-to-8 and 4-to-16 decoders. These use two, three or four binary input bits and provide four, eight or sixteen possible output lines respectively.

You can also test an enable input and switch between active-high and active-low output conventions. This makes the simulator useful for studying one-hot decoding, address decoding, chip selection and digital logic design.

How to Use the Binary Decoder Simulator

Choose the decoder size and toggle the input bits between zero and one. Keep enable E at 1 for normal active-high decoder operation, then press Simulate Binary Decoder.

3-to-8 decoder

Input:
A B C = 1 0 1

Binary:
101

Decimal:
5

Enabled:
E = 1

Active output:
Y5

Only the output whose index matches the binary input value becomes active.

What Is a Binary Decoder?

A binary decoder is a combinational circuit that converts a binary code into one of several mutually exclusive outputs. It can be viewed as the opposite conceptual operation of an encoder.

2 input bits
↓
2-to-4 decoder
↓
4 possible output lines

3 input bits
↓
3-to-8 decoder
↓
8 possible output lines

The number of outputs is normally 2 raised to the number of binary inputs.

2-to-4 Binary Decoder

A 2-to-4 decoder has two binary inputs and four outputs. Every possible 2-bit value activates a different output.

A	B	Decimal	Active Output
0	0	0	Y0
0	1	1	Y1
1	0	2	Y2
1	1	3	Y3

2-to-4 Decoder Truth Table

For an active-high decoder with E=1, exactly one output is high.

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

When the decoder is disabled, all active-high outputs become zero.

2-to-4 Decoder Boolean Expressions

With active-high inputs and enable E, the four outputs can be written as minterms of A and B.

Y0 = E AND NOT A AND NOT B

Y1 = E AND NOT A AND B

Y2 = E AND A AND NOT B

Y3 = E AND A AND B

Each output corresponds to one unique combination of the two input bits.

3-to-8 Binary Decoder

A 3-to-8 decoder uses three binary input bits to select one of eight outputs. The possible input values range from binary 000 through 111.

ABC = 000 → Y0
ABC = 001 → Y1
ABC = 010 → Y2
ABC = 011 → Y3
ABC = 100 → Y4
ABC = 101 → Y5
ABC = 110 → Y6
ABC = 111 → Y7

3-to-8 Decoder Example

Input:

A = 1
B = 0
C = 1

Binary:
101

Decimal:
5

Result:
Y5 = 1

All other outputs:
0

The binary input is interpreted as a numeric output address.

3-to-8 Decoder Boolean Equations

Y0 = E·A'·B'·C'
Y1 = E·A'·B'·C
Y2 = E·A'·B ·C'
Y3 = E·A'·B ·C
Y4 = E·A ·B'·C'
Y5 = E·A ·B'·C
Y6 = E·A ·B ·C'
Y7 = E·A ·B ·C

Each output is an individual minterm of the three binary variables.

4-to-16 Binary Decoder

A 4-to-16 decoder accepts a four-bit binary number and activates one of sixteen output lines.

Input range:

0000 → Y0
0001 → Y1
0010 → Y2
...
1010 → Y10
...
1111 → Y15

Four input bits can represent sixteen unique values because 2⁴ equals 16.

4-to-16 Decoder Example

Input:
1010

Decimal:
10

Enabled:
E = 1

Active output:
Y10

Active-high output vector:

0000010000000000

when displayed from Y15 down to Y0,
the 1 appears at the Y10 position.

Why a Decoder Produces 2ⁿ Outputs

Every input bit can have two states. With n independent binary inputs, there are 2ⁿ possible combinations.

Input Bits	Possible Codes	Decoder Type
1	2	1-to-2
2	4	2-to-4
3	8	3-to-8
4	16	4-to-16

What Is One-Hot Output?

A one-hot output means exactly one output line is asserted at a time. Standard active-high binary decoding naturally produces one-hot output when the decoder is enabled.

3-to-8 decoder

Input:
010

One-hot output:

Y0 = 0
Y1 = 0
Y2 = 1
Y3 = 0
Y4 = 0
Y5 = 0
Y6 = 0
Y7 = 0

Binary Input to Output Index

The decoder output index is simply the unsigned decimal value of the binary input code.

Binary:
110

Decimal conversion:
1×4 + 1×2 + 0×1
= 6

Decoder output:
Y6

This direct relationship makes decoders useful for selecting hardware resources based on binary addresses.

Decoder Enable Input

Many decoder circuits include an enable input. When the enable condition is not satisfied, normal decoding is suppressed.

Active-high enable:

E = 1
Decoder operates normally.

E = 0
Decoder disabled.

Active-high outputs:
all 0

The simulator uses an active-high enable input E.

Active-High Decoder Outputs

With active-high output logic, the selected output becomes 1 and all unselected outputs remain 0.

Input:
10

Active output:
Y2

Outputs:

Y0 = 0
Y1 = 0
Y2 = 1
Y3 = 0

Active-Low Decoder Outputs

Some decoder ICs use active-low outputs. In this convention, the selected output becomes 0 while unselected outputs remain 1.

Input:
10

Selected:
Y2

Active-low outputs:

Y0 = 1
Y1 = 1
Y2 = 0
Y3 = 1

Active-low signals are often indicated with a bar, bubble or slash in circuit diagrams and data sheets.

Decoder Output Minterms

Each decoder output represents exactly one minterm of the binary input variables. This makes binary decoders closely related to Boolean expression implementation.

2-bit input A,B

Y0 corresponds to:
A'B'

Y1:
A'B

Y2:
AB'

Y3:
AB

Using a Decoder to Implement Boolean Functions

Because each decoder output represents one minterm, selected outputs can be ORed together to implement a Boolean function expressed as a sum of minterms.

Function:

F(A,B,C) = Σm(1,3,5)

Using a 3-to-8 decoder:

F = Y1 OR Y3 OR Y5

This is one reason decoders are important in combinational logic design.

Binary Decoder vs Encoder

Device	Input	Output	Main Function
Binary Decoder	Compact binary code	One of many lines	Expand/decode code
Encoder	One of many input lines	Compact binary code	Encode input index

The two circuits perform complementary transformations, although their practical implementations may include additional enable, priority or valid signals.

Binary Decoder vs Demultiplexer

A decoder and demultiplexer can look similar because both use select information to activate one of multiple output paths.

Feature	Decoder	Demultiplexer
Binary select/address input	Yes	Yes
Separate routed data input	Usually no	Yes
One-of-many output	Yes	Yes
Main purpose	Decode code/address	Route data

Decoder Circuits in Memory Addressing

Binary decoders are commonly associated with address selection. A binary address can be decoded so only one memory row, register, device or functional block receives an active select signal.

3-bit address:

101

Decimal address:
5

3-to-8 decoder output:
Y5

Selected resource:
Resource 5

Decoder Circuits for Chip Select

A decoder can generate chip-select signals from address bits. Only the output associated with the current address becomes active, allowing one device to respond while others remain disabled.

Address bits:
A2 A1 A0

Decoder:
3-to-8

Possible device-select lines:
CS0 through CS7

Decoder Circuits in CPUs and Digital Systems

Decoders are used throughout digital systems for instruction decoding, register selection, memory addressing, control signal generation, display driving and resource selection.

A processor can decode instruction fields or addresses into individual control signals that activate particular internal paths.

Decoder Cascading

Larger decoder circuits can be built by combining smaller decoders and using enable inputs to activate the correct section.

Example concept:

Two 3-to-8 decoders
+
one higher-order select bit

can be arranged to produce
16 individually selectable outputs.

Practical cascading depends on the enable polarity and behavior of the specific decoder circuit or IC.

Decoder Truth Table and Minterm Relationship

Every row of a complete binary truth table corresponds to exactly one decoder output. For this reason, decoder output indices and Boolean minterm indices use the same binary numbering.

A B C = 1 1 0

Binary:
110

Minterm:
m6

Decoder output:
Y6

Common Binary Decoder Mistakes

A common mistake is reversing the significance of the input bits. In this simulator, A is the most significant input bit, followed by B, C and D as the decoder size increases.

Another mistake is expecting several outputs to be active at once. A normal binary decoder produces one selected output for each enabled input combination.

It is also important to distinguish active-high from active-low output logic. The selected line is 1 in active-high mode but 0 in active-low mode.

Binary Decoder Circuit Simulator Limitations and Notes

This simulator models ideal combinational 2-to-4, 3-to-8 and 4-to-16 binary decoders. It includes an active-high enable input and selectable active-high or active-low output behavior.

The tool does not model physical propagation delay, fan-out, electrical loading, unknown logic states, tri-state outputs or the detailed enable pin arrangements of specific commercial decoder ICs.

Input A is treated as the most significant bit. Therefore ABC=101 maps to decimal 5 and output Y5.

Binary Decoder Circuit Simulator FAQs

What is a binary decoder?

A binary decoder converts an n-bit binary input into one of 2ⁿ output lines.

What is a 2-to-4 decoder?

It accepts two binary inputs and selects one of four possible outputs.

What is a 3-to-8 decoder?

It accepts three input bits and activates one of eight outputs.

What is a 4-to-16 decoder?

It accepts a four-bit binary value and selects one of sixteen output lines.

Which output is active for binary 10 in a 2-to-4 decoder?

Binary 10 equals decimal 2, so output Y2 is selected.

Which output is active for 101 in a 3-to-8 decoder?

101 binary equals decimal 5, so Y5 is selected.

Which output is selected by binary 111?

In a 3-to-8 decoder, binary 111 selects Y7.

Which output does 1010 select in a 4-to-16 decoder?

1010 binary equals decimal 10, so Y10 is selected.

What is one-hot output?

It means exactly one output line is asserted while all other output lines remain inactive.

What does the decoder enable input do?

When the active-high enable input is 1, decoding operates normally. When it is 0, decoding is disabled.

What happens when an active-high decoder is disabled?

All outputs are zero.

What is an active-low decoder output?

The selected line becomes zero while unselected lines remain one.

How are decoder outputs related to minterms?

Each output corresponds to one Boolean minterm of the decoder’s binary input variables.

Can a decoder implement Boolean functions?

Yes. Decoder outputs corresponding to selected minterms can be combined, often with an OR gate, to implement a Boolean function.

What is the difference between a decoder and encoder?

A decoder expands a binary code into one of many outputs, while an encoder converts one of many input lines into a compact binary code.

What is the difference between a decoder and demultiplexer?

A demultiplexer routes a separate data input to a selected output, while a decoder primarily activates an output based on a binary code.