Design and Use of Encoders

Design and Use of Encoders

An encoder is a combinational logic circuit that converts an active signal from a set of inputs into a coded output. Encoders are used in a variety of applications where there is a need to reduce the number of bits required to represent a given input combination. The output typically represents the binary code corresponding to the position of the active input.

Types of Encoders

There are several types of encoders, but the most common are:

1. Binary Encoder: A binary encoder has $2^n$ input lines and $n$ output lines, where $n$ is the number of bits required to represent the number of inputs. The output generates the binary representation of the active input line.

2. Priority Encoder: A priority encoder is an extension of a binary encoder that resolves conflicts when multiple inputs are active. The encoder outputs the binary code of the highest-priority active input (usually the highest numbered active input).

3. Decimal-to-Binary Encoder: This encoder converts 10 decimal inputs (0-9) into 4-bit binary numbers.

Basic Concept of an Encoder

An encoder takes multiple input lines (often labeled $I_0, I_1, I_2, ..., I_n$) and produces a smaller number of output lines (usually labeled $O_0, O_1, O_2, ..., O_m$), where the number of output lines $m$ is enough to represent the binary code for each active input line.

The key idea behind encoders is that only one input is active at a time, or if multiple inputs are active, the highest-numbered input is selected in a priority encoder.

1. Binary Encoder

A binary encoder typically has $2^n$ input lines and $n$ output lines. Each of the $2^n$ input lines corresponds to a unique binary code on the output.

Example: 4-to-2 Binary Encoder

For a 4-input encoder, the inputs are labeled as $I_0, I_1, I_2, I_3$, and the outputs are $O_0, O_1$. When one input is active, the encoder converts the active input into a 2-bit binary output.

Truth Table:

Input $I_3$	Input $I_2$	Input $I_1$	Input $I_0$	Output $O_1$	Output $O_0$
0	0	0	1	0	0
0	0	1	0	0	1
0	1	0	0	1	0
1	0	0	0	1	1

• Input $I_3$ is the highest priority. If multiple inputs are active, the encoder will output the binary code for the highest active input.

Logic Equation for 4-to-2 Encoder:

• $O_1 = I_2 + I_3$
• $O_0 = I_1 + I_3$

2. Priority Encoder

A priority encoder assigns priorities to inputs. When multiple inputs are active simultaneously, the encoder will output the binary code corresponding to the highest-numbered input.

Example: 4-to-2 Priority Encoder

In a 4-to-2 priority encoder, the inputs are $I_0, I_1, I_2, I_3$, and the outputs are $O_1, O_0$. If multiple inputs are active, the highest priority input is encoded.

Truth Table:

Input $I_3$	Input $I_2$	Input $I_1$	Input $I_0$	Output $O_1$	Output $O_0$	Valid
0	0	0	0	0	0	0
0	0	0	1	0	0	1
0	0	1	0	0	1	1
0	1	0	0	1	0	1
1	0	0	0	1	1	1

• Input $I_3$ has the highest priority. If $I_3 = 1$, the encoder will output $O_1 O_0 = 11$, regardless of the state of the other inputs.

Logic Equations for Priority Encoder:

• $O_1 = I_2 + I_3$
• $O_0 = I_1 + I_3$

The valid output is typically included in a priority encoder to indicate whether the output is valid or not. It is 1 when any input is active and 0 when no input is active.

3. Decimal-to-Binary Encoder

This encoder is used to convert decimal digits (0-9) to a 4-bit binary number. A 10-input encoder is needed for this conversion, with the inputs corresponding to the decimal digits.

Example: Decimal-to-Binary Encoder (10-to-4 Encoder)

Truth Table:

Decimal Input	Binary Output
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

This encoder provides a direct mapping between decimal values and binary codes.

Applications of Encoders

1. Data Compression: Encoders can reduce the number of bits needed to represent input data, making them useful in compression algorithms.
2. Keypads: A keypad encoder can convert the row-column signals from a keypress into a unique binary code representing the key pressed.
3. Digital Communication: In digital communication systems, encoders are used to convert the input signals into a code that is easier to transmit or store.
4. Priority Circuits: In applications where priority is important, such as in interrupt handling in processors, priority encoders are used to determine the highest-priority interrupt.
5. Rotary Encoders: Used in motion sensing devices, they translate the rotational position into a binary code.

Design of an Encoder

1. Determine Inputs and Outputs: Decide on the number of input lines and the number of output lines based on the encoding requirement.

   • For example, a 4-to-2 encoder has 4 inputs and 2 outputs.

2. Define the Encoder Function: Write the truth table for the encoder, specifying how each input combination is converted into the binary output.

3. Simplify Logic Equations: Use Boolean algebra or Karnaugh maps to simplify the logic expressions for the output lines.

4. Implement the Logic: Use logic gates like AND, OR, NOT, and XOR gates to implement the simplified Boolean equations.

Conclusion

Encoders are fundamental components in digital systems, used to convert information from one form (often multiple active lines) to a more efficient or compact form (usually fewer output lines). The design of encoders depends on the specific encoding scheme, and the applications range from keypads to digital communication systems and priority circuits. The encoder's ability to reduce the number of bits used to represent data makes it a crucial part of digital logic design.