Decoder
Overview
Decoders are combinational circuits that convert coded inputs into a specific output line. They are commonly used in memory addressing, data routing, and instruction decoding in microprocessors. A typical n-to-2ⁿ decoder takes n input lines and activates one of the 2ⁿ outputs based on the binary value of the inputs.
Detailed Explanation
Operation Principle
For an n-to-2ⁿ decoder:
- Only one output is active for any input combination.
Example (2-to-4 decoder):
Inputs: A, B
Outputs: Y0, Y1, Y2, Y3 with:
Y0 = A'B'
Y1 = A'B
Y2 = AB'
Y3 = AB
Circuit Design
1. Use AND gates for each output.
2. Invert inputs as necessary to match the required minterm.
Applications
- Memory address decoding
- Data multiplexing
- Control signal generation in microprocessors
Practice Problems
- Design a 3-to-8 decoder.
- Show the truth table and corresponding Boolean expressions for each output of a 2-to-4 decoder.
- Implement a decoder using only NAND gates.
References
- Digital Logic Design by Morris Mano
- Decoder Tutorial