Decoders – Dr. Balvinder Taneja

Decoders: A Detailed Discussion

A Decoder is a combinational logic circuit that takes a binary code as input and decodes it into a unique output. Essentially, a decoder takes n-bit input and activates one of the 2^n output lines corresponding to the input binary value.

🧠 Introduction to Decoders

A Decoder performs the reverse operation of an Encoder. While an Encoder takes multiple inputs and produces a binary code output, a Decoder takes a binary code and decodes it to produce a one-hot output (only one output is high at a time).

Inputs: The number of input lines is typically n bits.
Outputs: The number of output lines is 2^n.

In simpler terms, a Decoder “decodes” the binary value input into a unique output.

🎯 Types of Decoders

There are two main types of Decoders:

Binary Decoder
BCD (Binary-Coded Decimal) Decoder

1️⃣ Binary Decoder

A Binary Decoder takes an n-bit input and generates 2^n output lines, where each output corresponds to one of the possible input combinations.

Example: 3-to-8 Binary Decoder

A 3-to-8 Decoder has:

3 input lines (I₂, I₁, I₀)
8 output lines (O₇ to O₀)

For each combination of the 3-bit input, one of the 8 output lines is activated.

Truth Table for 3-to-8 Decoder:

I₂	I₁	I₀	O₇	O₆	O₅	O₄	O₃	O₁	O₀
0	0	0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0	1	0
0	1	0	0	0	0	0	1	0	0
0	1	1	0	0	1	0	0	0	0
1	0	0	0	1	0	0	0	0	0
1	0	1	1	0	0	0	0	0	0
1	1	0	0	0	1	0	0	0	0
1	1	1	0	0	0	1	0	0	0

Inputs: I₂, I₁, I₀
Outputs: O₇, O₆, O₅, O₄, O₃, O₂, O₁, O₀

For example:

If the input is 000, then only O₀ is active.
If the input is 010, then only O₂ is active.

In this way, a Binary Decoder translates a binary code into a one-hot output.

2️⃣ BCD (Binary-Coded Decimal) Decoder

A BCD Decoder is a specific type of decoder used to decode a 4-bit binary-coded decimal (BCD) number. A BCD number represents a decimal digit (0-9) in 4-bit binary form.

It takes 4-bit input and produces 10 outputs (one for each decimal digit 0-9).
The output is active high for the binary representation of the decimal number.

Example: 4-to-10 BCD Decoder

A 4-to-10 BCD Decoder has:

4 input lines (I₃, I₂, I₁, I₀)
10 output lines (O₉ to O₀)

Each 4-bit input corresponds to a decimal digit from 0 to 9, and one of the 10 output lines is activated.

Truth Table for 4-to-10 BCD Decoder:

I₃	I₂	I₁	I₀	O₉	O₈	O₇	O₆	O₅	O₄	O₂	O₁	O₀
0	0	0	0	0	0	0	0	0	0	0	0	1
0	0	0	1	0	0	0	0	0	0	0	1	0
0	0	1	0	0	0	0	0	0	0	1	0	0
0	0	1	1	0	0	0	0	0	1	0	0	0
0	1	0	0	0	0	0	1	0	0	0	0	0
0	1	0	1	0	0	1	0	0	0	0	0	0
0	1	1	0	0	1	0	0	0	0	0	0	0
0	1	1	1	1	0	0	0	0	0	0	0	0
1	0	0	0	0	0	0	0	1	0	0	0	0
1	0	0	1	0	0	0	0	0	1	0	0	0

For example:

When the input is 0000, the output O₀ is active (representing the decimal value 0).
When the input is 0001, the output O₁ is active (representing the decimal value 1), and so on.

⚙️ Working of Decoders

1. Basic Working:

A decoder takes a binary input and converts it to a corresponding one-hot output. Only one output line is active for each input combination.

2. How a Binary Decoder Works:

In a Binary Decoder, the input binary value determines which output line is activated.
For example, in a 3-to-8 decoder, the 3-bit input selects one of the 8 output lines. If the input is 011, the O₃ output will be activated.

3. How a BCD Decoder Works:

A BCD decoder works similarly, but it maps a 4-bit binary input to one of the 10 outputs representing the decimal digits from 0 to 9.

🎯 Applications of Decoders

Memory Addressing: Decoders are used to select specific memory locations based on the address input.
7-segment Display: Decoders are often used to drive 7-segment displays, converting binary codes into the corresponding signals needed to light up the display segments.
Digital Communication: Decoders are used in communication systems to decode received signals back into readable data.
Instruction Decoding in CPUs: Decoders are used in processors to decode the instruction opcodes.

📝 Summary

Feature	Decoder
Function	Converts binary code to one-hot output
Inputs	n bits
Outputs	2^n output lines
Types	Binary Decoder, BCD Decoder
Applications	Memory addressing, 7-segment display, instruction decoding

🌟 Key Takeaways:

Decoders are used to convert a binary input into a corresponding one-hot output.
Binary decoders handle general n-bit inputs and produce 2^n outputs.
BCD decoders are specific to converting 4-bit BCD numbers to the corresponding decimal output.