Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL

7.4 LOGIC DESIGN WITH MULTIPLEXERS

The main function of a multiplexer is to route only one selected data input to its single output. Because of its unique structure, a multiplexer can also be used to implement a logic function. Consider the 4: 1 multiplexer circuit illustrated in Figure 7.12. The truth table of the circuit identifies the function of the circuit as the AND logic function. In fact, any logic function with N variables can be implemented directly with a 2^N : 1 multiplexer. The data inputs of the multiplexer are the function values, and the select inputs are the variables of the function. However, complex functions make their direct implementation with multiplexers impractical. Fortunately, it is possible to design logic functions with smaller size multiplexers by identifying patterns between the function and its variables in the truth table. Consider again the truth table in Figure 7.12. The truth table can be organized by selecting x₁ select inputs and relating the data input x₂ to the function as illustrated in Figure 7.13. Therefore, the AND function can be implemented using a 2 : 1 multiplexer with additional connections and logic gates when necessary.

Figure 7.12 AND Logic Function Implementation with a 4: 1 Multiplexer

Figure 7.13 AND Logic Function Implementation ...