Encoders in Digital Logic: Converting Inputs to Binary Codes

Understand the functionality and design of encoders in digital logic circuits. This guide explains how encoders convert multiple input lines into a binary output code, providing detailed diagrams and Boolean expressions illustrating their operation and use in digital systems.

Encoders in Digital Logic

What is an Encoder?

An encoder is a combinational logic circuit that converts a set of input lines into a binary code. It's the inverse operation of a decoder. An encoder takes multiple input lines and produces a smaller number of output lines representing the active input.

4-to-2 Line Encoder

A 4-to-2 line encoder has four input lines (A₃, A₂, A₁, A₀) and two output lines (D₁, D₀). Only one input line can be high (1) at any given time; the output lines represent the binary code of the active input.

Block Diagram

(A block diagram of a 4-to-2 line encoder should be included here. The four input lines (A₃, A₂, A₁, A₀) and two output lines (D₁, D₀) should be clearly labeled.)

Truth Table

Boolean Expressions

The Boolean expressions for the outputs are:

• D₁ = A₃ + A₂
• D₀ = A₃ + A₁

(A circuit diagram implementing this 4-to-2 encoder using OR gates would be helpful here.)

8-to-3 Line Encoder

An 8-to-3 line encoder takes eight input lines and generates a 3-bit binary code. Only one input can be active at a time.

Block Diagram

(A block diagram of an 8-to-3 line encoder would be included here.)

Truth Table

Boolean Expressions

The Boolean expressions for the outputs are:

• x = D₄ + D₅ + D₆ + D₇
• y = D₂ + D₃ + D₆ + D₇
• z = D₁ + D₃ + D₅ + D₇

(A circuit diagram implementing this 8-to-3 encoder using OR gates would be helpful here.)

Conclusion

Encoders are essential components in digital systems for converting multiple input lines into a compact binary representation. Understanding their operation and design is key to many digital systems.