Notes on Decoders

Introduction

• Decoders are combinational circuits with N inputs and M outputs.
• Only one output is high at any given time, depending on the input combination.
• For N binary inputs:
  • Total combinations = 2^N
  • Maximum outputs (M) = 2^N

Examples

• 3 to 8 Decoder: 3 inputs, 8 outputs (M = 2^3)
• 4 to 16 Decoder: 4 inputs, 16 outputs (M = 2^4)
• BCD to Decimal Decoder: 4 inputs, 10 outputs (M < 2^4)

General Characteristics

• M is less than or equal to 2^N.
• Only one output is high at any time based on input combinations.

Applications of Decoders

1. Code Conversion

   • E.g., 3 to 8 decoder for binary to octal conversion.
   • BCD to decimal decoder converts BCD to decimal.

2. Address Decoding

   • Used in processors to access multiple memory chips.
   • Example: Each memory chip = 256 bytes accessed via 8 address lines using 2 to 4 decoder.

3. Control Signal Generation

   • Outputs can control peripheral devices or internal functions.

4. Logic Circuit Implementation

   • Can implement different logic circuits using OR gates with outputs from the decoder.

Designing a Decoder

3 to 8 Decoder Logic Circuit

• Requires 3 inputs, 8 outputs.
• E.g., D0 is high when A, B, and C are all low:
  • D0 = A'B'C'
  • D3 = A'BC
  • D7 = ABC
• Total of 8 AND gates needed for implementation.

Enable Input

• Active high: Decoder enabled when enable input is high
• Active low: Decoder enabled when enable input is low
• Logic circuit includes an enable input for 3 to 8 decoder design.

BCD to Decimal Decoder

• Truncated version of 4 to 16 decoder with 4 inputs, 10 outputs.
• Valid input combinations yield high outputs.

Constructing Higher Order Decoders

• Higher order decoders (e.g., 4 to 16 or 5 to 32) can be built using lower order decoders.
• Example: 4 to 16 using two 3 to 8 decoders:
  • Two outputs from each 3 to 8 decoder combine to form 16 outputs.
  • MSB (A3) selects which decoder to enable.
• Example: 5 to 32 decoder uses four 3 to 8 decoders and one 2 to 4 decoder for selection.

Implementing Logic Functions with Decoders

• Example: Implementing a full adder using a 3 to 8 decoder.
  • Sum output high for specific combinations (D1, D2, D4, D7).
  • Carry output high for specific combinations (D3, D5, D6, D7).
• Use OR gates to combine outputs for which the desired output is high.

Handling Many Outputs

• For logic circuits with many high outputs, combine via multiple OR gates or use NOR gates to combine low outputs to generate desired results.

Conclusion

• Decoders are essential for code conversion, address decoding, control signal generation, and implementing logic circuits.
• Understanding their design and applications is crucial for electronics.
• Questions and suggestions can be directed to the comment section.