MUX / DEMUX Cheat Sheet
This cheat sheet summarizes the key formulas, select line calculations, and combination methods for Multiplexers (MUX) and Demultiplexers (DEMUX).
1. Multiplexer (MUX)
A MUX selects one input from multiple inputs based on select lines.
Inputs: I₀, I₁, ..., IN-1
Output: Y
Select lines: S₀, S₁, ..., Sn-1
Output: Y
Select lines: S₀, S₁, ..., Sn-1
Minimum Number of Select Lines
To select N inputs:
n = ⌈log₂ N⌉
Example: 8 inputs → n = log₂ 8 = 3 select lines
Boolean Expression
Y = Σ Ii · mi(S), i = 0..N-1
Where mi(S) = minterm for select lines corresponding to input Ii
Example: 4-to-1 MUX (S₁, S₀)
Y = I₀·¬S₁¬S₀ + I₁·¬S₁S₀ + I₂·S₁¬S₀ + I₃·S₁S₀
Combination Methods for MUX
- Cascading MUX: Combine smaller MUXs to form larger MUX (e.g., two 4-to-1 + one 2-to-1 → 8-to-1 MUX)
- Parallel MUX: Multiple MUXs in parallel for multi-bit channels
2. Demultiplexer (DEMUX)
A DEMUX routes one input to one of many outputs based on select lines.
Input: I
Outputs: Y₀, Y₁, ..., YN-1
Select lines: S₀, S₁, ..., Sn-1
Outputs: Y₀, Y₁, ..., YN-1
Select lines: S₀, S₁, ..., Sn-1
Minimum Number of Select Lines
To control N outputs:
n = ⌈log₂ N⌉
Example: 8 outputs → n = 3 select lines
Boolean Expression
Yi = I · mi(S), i = 0..N-1
Example: 1-to-4 DEMUX (S₁, S₀)
Y₀ = I·¬S₁¬S₀, Y₁ = I·¬S₁S₀, Y₂ = I·S₁¬S₀, Y₃ = I·S₁S₀
Combination Methods for DEMUX
- Cascading DEMUX: Smaller DEMUXs combined to form larger DEMUX (e.g., two 1-to-4 → 1-to-8 DEMUX)
- Parallel DEMUX: For multi-bit inputs, use multiple DEMUXs in parallel
3. Quick Reference Table
| Device | Inputs | Outputs | Select Lines | Boolean Expression |
|---|---|---|---|---|
| MUX | N | 1 | n = ⌈log₂ N⌉ | Y = Σ Ii · mi(S) |
| DEMUX | 1 | N | n = ⌈log₂ N⌉ | Yi = I · mi(S) |
4. Summary
- MUX: many inputs → one output; selects input based on select lines
- DEMUX: one input → many outputs; routes input to output based on select lines
- Use cascading to scale for larger N
- Use parallel MUX/DEMUX for multi-bit data
- Exact minterm placement ensures correct routing