Overview
This lecture introduces multiplexers (MUX), a combinational circuit that selects and routes binary data from multiple inputs to a single output using select lines.
Introduction to Multiplexers
- A multiplexer (MUX) is a combinational circuit that selects one binary input from many and directs it to the single output.
- Multiplexers are also known as data selectors.
- The selection of inputs is controlled by select lines or selector variables.
- For four input lines, there are two selector variables: S0 (least significant bit) and S1 (most significant bit).
- The number of outputs in any multiplexer is always one, regardless of the number of inputs.
Representation and Structure
- Multiplexers are depicted as a rectangular box with inputs, a single output, and select lines.
- A 2-to-1 MUX has two inputs, one output, and one select line.
- General form: For n inputs, the number of select lines m = log₂(n).
Selector Variables and Input Relationship
- If n = 2^m, then m is the number of select lines for n inputs.
- Example: For 4 inputs, m = log₂4 = 2; thus, two select lines (S0 and S1).
Advantages of Multiplexers
- Reduces the number of wires and gates required in combinational circuits.
- Simplifies circuit complexity and reduces cost.
- Facilitates implementation of various combinational circuits using a single MUX IC.
- Commonly used to implement logical expressions and circuits (e.g., adders, subtractors).
Types of Multiplexers
- Types include 2-to-1, 4-to-1, 8-to-1, 16-to-1, and 32-to-1 multiplexers.
- The output is always one; the number preceding "to-1" indicates the input lines.
- Number of select lines increases logarithmically: 2-to-1 (1 select), 4-to-1 (2), 8-to-1 (3), 16-to-1 (4), 32-to-1 (5).
2-to-1 Multiplexer Details
- Represented as a rectangle with inputs I0, I1, output Y, one select line (S), and enable signal (E).
- Truth table: If E = 0, Y = 0 (regardless of S); if E = 1 and S = 0, Y = I0; if E = 1 and S = 1, Y = I1.
- Logic equation: Y = E·(S̅·I0 + S·I1)
- Implementation: Uses two AND gates (for S̅I0 and SI1, both ANDed with E), outputs combined with one OR gate.
Key Terms & Definitions
- Multiplexer (MUX) — A device that selects one input from multiple sources and forwards it to an output.
- Select Line (Selector Variable) — Controls which input is routed to the output.
- Enable (E) — A control signal that activates or deactivates the MUX output.
- Truth Table — Table defining the output for all possible input combinations.
- Logic Expression — Boolean formula representing circuit output.
Action Items / Next Steps
- Review the truth table and logic equation for 2-to-1 multiplexer.
- Prepare to study implementation and function of larger multiplexers (4-to-1, 8-to-1, etc.).
- Practice drawing and analyzing basic MUX circuits.