Lecture 8: Decoders & Logic Implementation

1. What is a Decoder?

• A Combinational Circuit that converts binary input information into a unique output signal.
• For n inputs, it has a maximum of $2^n$ unique outputs.
• Exactly one output line is active (typically 1) at any time, based on the input combination.

2. 3-to-8 Decoder

• Inputs: A, B, C.
• Outputs: $y_0, y_1, ..., y_7$.
• If input is 000 (decimal 0), then $y_0 = 1$ and all others are 0.
• If input is 101 (decimal 5), then $y_5 = 1$.

3. Logic Implementation

• A decoder acts as a Minterm Generator. Every output corresponds to one minterm ($y_i = m_i$).
• To implement any Boolean function:
  1. Get the minterm list ($\sum m$).
  2. Use a decoder with the required number of inputs.
  3. Connect the specified outputs ($y_i$) to an OR gate.