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Multiplexer and 4:1 MUX
Short answer
A multiplexer (MUX) is a combinational circuit that selects one of many inputs to a single output under select lines. A 4:1 MUX has four data inputs (I0-I3), two selects (S1,S0), and output Y = S1'S0'I0 + S1'S0 I1 + S1 S0' I2 + S1 S0 I3. Implemented with inverters, AND gates and an OR gate.
What is multiplexer (MUX)? Explain 4:1 Multiplexer.
A multiplexer (MUX) is a combinational circuit that selects one of many input lines and sends it to a single output line, under the control of select lines. It is also called a "data selector". A 2ⁿ:1 MUX has 2ⁿ data inputs, n select lines and one output.
4:1 multiplexer
It has four data inputs (I0 to I3), two select lines (S1, S0) and one output Y.
+-----------+
I0 -----|0 |
I1 -----|1 4:1 |
I2 -----|2 MUX |---- Y
I3 -----|3 |
+--+----+---+
| |
S1 S0
Function table
| S1 | S0 | Y |
|---|---|---|
| 0 | 0 | I0 |
| 0 | 1 | I1 |
| 1 | 0 | I2 |
| 1 | 1 | I3 |
Boolean expression:
Y = S1'S0' I0 + S1'S0 I1 + S1 S0' I2 + S1 S0 I3
Gate implementation: two NOT gates for S1' and S0'; four 3-input AND gates, each combining one input with its matching select combination; and one 4-input OR gate to give Y.
I0 -[AND: S1' S0']--+
I1 -[AND: S1' S0 ]--+--[OR]-- Y
I2 -[AND: S1 S0']--+
I3 -[AND: S1 S0 ]--+
Applications: data routing, parallel-to-serial conversion, implementing Boolean functions, and communication systems (time-division multiplexing).
✓ Answer checked by Claude Opus 5.5 (high effort)
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