Decoders in Digital Logic: Binary Code to Output Line Conversion

Understand the functionality and design of decoders in digital logic circuits. This guide explains how decoders convert binary input codes into activated output lines, providing detailed diagrams and truth tables illustrating their operation and applications in various digital systems.

Decoders in Digital Logic

What is a Decoder?

A decoder is a combinational logic circuit that converts a binary code (a set of bits) into a set of output lines. Only one output line is active (high or 1) at any given time, indicating the specific binary combination present at the input. It's a many-to-one mapping from binary codes to output lines.

n-to-m Decoders

An n-to-m decoder has n input lines and m output lines, where m ≤ 2ⁿ. The n input lines represent a binary code, and exactly one of the m output lines is activated based on the input code.

Example: 3-to-8 Line Decoder

(A block diagram of a 3-to-8 line decoder should be included here. The three input lines (x, y, z) and eight output lines (D₀-D₇) should be clearly labeled. The three inverters providing the complemented inputs should also be shown.)

Truth Table for a 3-to-8 Line Decoder

2-to-4 Line Decoder using NAND Gates

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Building Larger Decoders

Larger decoders can be constructed by combining smaller decoders. For example, a 3-to-8 decoder can be implemented using two 2-to-4 decoders.

(A diagram illustrating a 3-to-8 decoder built from two 2-to-4 decoders should be included here.)

Conclusion

Decoders are essential components in digital systems for converting binary codes into individual output signals. They're used in a wide range of applications, from selecting memory locations to driving displays.