Encoder / Decoder Calculator

What are Encoders and Decoders?

Encoders and decoders are complementary digital circuits. Encoders convert multiple input lines into fewer output lines with binary codes, while decoders perform the reverse operation, converting binary codes back into individual output lines.

How to Use This Calculator

Select circuit type - Choose 8×3 Encoder or 3×8 Decoder
Set input values - Configure input lines or address bits
Click "Calculate" to see encoded/decoded outputs
View results including truth table and Boolean expressions
Copy or export the analysis for your projects

8×3 Priority Encoder

What is a Priority Encoder?

An 8×3 priority encoder has 8 input lines (I0-I7) and produces a 3-bit binary output representing the highest priority active input. Higher numbered inputs have higher priority.

Boolean Expressions

Y0 = I1 + I3 + I5 + I7 (LSB)
Y1 = I2 + I3 + I6 + I7
Y2 = I4 + I5 + I6 + I7 (MSB)

3×8 Binary Decoder

What is a Binary Decoder?

A 3×8 decoder has 3 address inputs (A0-A2) and 8 output lines (Y0-Y7). Only one output is active (high) at a time, corresponding to the binary address.

Operation

Address 000: Y0 = 1, all others = 0
Address 001: Y1 = 1, all others = 0
Address 010: Y2 = 1, all others = 0
And so on...

Applications and Uses

Encoders

Keyboard encoding
Priority interrupt systems
Data compression
Position encoding

Decoders

Memory address decoding
Instruction decoding in CPUs
Display drivers
Device selection

Examples & Worked Problems

Example 1: Priority Encoder

Problem: Inputs I2=1, I5=1, I7=0. What is the output?

Solution:

I5 has higher priority than I2
Binary representation of 5 is 101
Output: Y2=1, Y1=0, Y0=1

Example 2: Binary Decoder

Problem: Address A2=1, A1=0, A0=1. Which output is active?