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Designing Larger Muxes (4-to-1 and 8-to-1)

Digital Logic Systems: From Zero to Hero

24. Designing Larger Muxes (4-to-1 and 8-to-1)

Larger Muxes are built on the same principle: generating a unique enable signal for the single data path we wish to select.

4-to-1 Multiplexer

  • Inputs: $D_0, D_1, D_2, D_3$ (4 data inputs)
  • Select Lines: $S_1, S_0$ (2 select lines, $2^2=4$)

Logic Equation: $$Y = \overline{S_1}\overline{S_0} D_0 + \overline{S_1}S_0 D_1 + S_1\overline{S_0} D_2 + S_1 S_0 D_3$$

This requires four 3-input AND gates and one 4-input OR gate.

Mux Implementation of Boolean Functions

A powerful use of Muxes is implementing any Boolean function directly from its truth table.

Example: 3-variable function using an 8-to-1 Mux

  1. Connect the function variables (A, B, C) to the three select lines ($S_2, S_1, S_0$).
  2. For each minterm $m_i$ where the output is 1, connect the corresponding data input $D_i$ to logic HIGH (1).
  3. For all other data inputs $D_j$, connect them to logic LOW (0).

This method requires zero logic gates other than the Mux itself, making it highly efficient for complex functions.