Encoders

An encoder is a digital combinational circuit that converts multiple input signals into a binary code. It typically has one active input at a time and generates a binary output representing the position of that active input.

• The number of inputs is usually 2ⁿ, with n output lines.
• Inputs are usually active high, meaning high voltage represents an active signal.
• Binary-weighted encoders assign codes based on input position using binary values.
• Encoders help convert parallel inputs into compact binary formats for processing.
• Encoders are useful in digital systems for data compression and efficient transmission.
• For example, a 4-to-2 encoder has four inputs and produces a 2-bit output code.

Types of Encoders

1. 4 to 2 Encoder

The 4 to 2 Encoder consists of four inputs Y₃, Y₂, Y₁ & Y₀, and two outputs A₁ & A₀. At any time, only one of these 4 inputs can be ‘1’ in order to get the respective binary code at the output. The figure below shows the logic symbol of the 4 to 2 encoder.

Truth Table

The Truth table of 4 to 2 encoders is as follows:

Logical expression for A₁ and A₀:

A₁ = Y₃ + Y₂
A₀ = Y₃ + Y₁

Circuit Diagram

The above two Boolean functions A₁ and A₀ can be implemented using two input OR gates: 

2. Octal to Binary Encoder (8 to 3 Encoder)

The 8 to 3 Encoder or octal to Binary encoder consists of 8 inputs: Y₇ to Y₀ and 3 outputs: A₂, A₁ & A₀. Each input line corresponds to each octal digit value and three outputs generate corresponding binary code. The figure below shows the logic symbol of octal to the binary encoder.

Truth Table

Logical expression for A₂, A₁, and A₀:

A₂ = Y₇ + Y₆ + Y₅ + Y₄
A₁ = Y₇ + Y_{6 +} Y₃ + Y₂
A₀ = Y₇ + Y₅ + Y₃ + Y₁

Circuit Diagram

The above three Boolean functions A₂, A₁, and A₀ can be implemented using four input OR gates:

3. Decimal to BCD Encoder

The decimal-to-binary encoder usually consists of 10 input lines and 4 output lines. Each input line corresponds to each decimal digit and 4 outputs correspond to the BCD code. This encoder accepts the decoded decimal data as an input and encodes it to the BCD output which is available on the output lines. The figure below shows the logic symbol of the decimal to BCD encoder.

Truth Table

Logical expression for A₃, A_2, A_1, and A₀:

A₃ = Y₉ + Y₈
A₂ = Y₇ + Y₆ + Y₅ +Y₄
A₁ = Y₇ + Y₆ + Y₃ +Y₂
A₀ = Y₉ + Y₇ +Y₅ +Y₃ + Y₁

Circuit Diagram

The above two Boolean functions can be implemented using OR gates:

4. Priority Encoder

A 4 to 2 priority encoder has 4 inputs: Y₃, Y₂, Y₁ & Y₀, and 2 outputs: A₁ & A₀. Here, the input, Y₃ has the highest priority, whereas the input, Y₀ has the lowest priority. In this case, even if more than one input is ‘1’ at the same time, the output will be the (binary) code corresponding to the input, which is having higher priority.

Truth Table

Logical Expressions using K-Map

The logical expression for A₁ is shown below:

The Logical Expression for A₀ is shown below:

Circuit Diagram

The above two Boolean functions can be implemented as:

Errors in Encoders

There is an ambiguity, when all outputs of the encoder are equal to zero.

• If more than one input is active High, then the encoder produces an output, which may not be the correct code.
• In a simple encoder, when all inputs are LOW, the output is 0. This creates confusion because the output 0 may also represent a valid input (for example, input line 0 active).
• Basic encoders cannot determine which input to encode if multiple inputs are HIGH at the same time, leading to unpredictable or incorrect outputs.

So, to overcome these difficulties, we should assign priorities to each input of the encoder. Then, the output of the encoder will be the code corresponding to the active high inputs, which have higher priority.