Multiplexers in Digital Systems Fundamentals

ECE 352 Digital System Fundamentals Multiplexers Multiplexers 1 1

Multiplexers (Muxes) Selection: based on the select inputs, choose one from several data inputs to drive an output Output is equal to one of the data inputs Select inputs indicate which data input Typically: n select lines, 2ndata input lines MUX 2:1 1 0 Output Multiplexers Data Inputs and Labels Select Input MUX 2:1 MUX 2:1 B A B 1 1 A B A 0 0 0 1 2 2

Multiplexer Labeling Data inputs must be labeled to indicate which is selected for a given select value Select inputs must be labeled so we know the ordering of bits within the select value Exception: if there is only one select bit MUX 4:1 3 2 1 0 1 Multiplexers 0 Data Inputs and Labels Select Inputs and Labels 3 3

Multiplexer Structure Can always build things by understanding their truth tables and then building the logic functions 2:1 multiplexer with 1-bit select signal S Multiplexers Y = S D1 + S D0 4:1 multiplexer with 2-bit select S Y = S1 S0 D3 + S1 S0 D2 + S1 S0 D1 + S1 S0 D0 4 4

Multiplexer Logic Function The two-level logic function for any mux output Y is really quite easy to remember Write an OR of all minterms of the select inputs AND each minterm with the corresponding data input Example: An 8-to-1 mux has a 3-bit select input S = S2S1S0 Multiplexers = + + + Y m (S) D m (S) + D m (S) + D m (S) + D 0 0 1 D 1 2 2 3 3 + m (S) m (S) D m (S) D m (S) D 4 4 5 5 6 6 7 7 = + + + Y S S S + D S S S + D S S S D S S S D 2 1 0 0 2 1 0 1 2 1 0 2 2 1 0 3 + + S S S D S S S D S S S D S S S D 2 1 0 4 2 1 0 5 2 1 0 6 2 1 0 7 5 5

Other Ways To Build Muxes Decode select signals into individual enables for each data input Build larger muxes using smaller muxes Repeated refinement of the selection code Multiplexers D3 1 D2 0 1 Y 0 D1 1 D0 0 S0 S1 First-level muxes each choose an input based on select bit 0, select bit 1 chooses between the results 6 6

Hierarchical Mux Example D3 1 D3 D2 0 Multiplexers 1 Y D1 0 D1 1 D1 D0 0 1 S0 0 S1 7 7

Concept: Value-Fixing Can set one or more inputs of a logic circuit to a constant (fixed) value (meaning, 0 or 1) We might do this to make the logic circuit behave in a particular way Example: set one input of a 2-input XOR gate to 1 to make the XOR act like an inverter Example: set one input of a 3-to-8 decoder to 0 to make the 3-to-8 decoder act like a 2-to-4 decoder Need to make sure to use the correct 4 outputs based on which input was set to 0! Example: implement a logic function with a multiplexer by fixing multiplexer data inputs This is how the FPGAs used in this class implement logic Multiplexers 8 8

Example: Logic With Muxes B 1 + B 1 = 1 1 D3 1 1 A 1 + A B = A + B 1 D2 0 Truth Table Multiplexers 1 Y 0 1 D1 1 B 0 D0 0 B S0 Function Inputs B 1 + B 0 = B A S1 9 9

Example: Logic With Muxes F = A BC + AB + AB C MUX 4:1 A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 C C 3 2 1 0 1 Multiplexers 0 1 C 1 F 0 0 C AB Identify what function is for each set of AB values 10 10

ECE 352 Digital System Fundamentals Multiplexers Multiplexers 11 11