In the post 2x1 mux using NAND gates, we discussed how we can use NAND gates to build a 2x1 multilexer. In this post, we will discuss how we can use NAND gates to build a 4x1 mux:
1. Using structural approach: As we know that a 4x1 mux can be structurally built from 2x1 muxes as shown in figure 1 below. Thus, in the same way, we can arrange the 2-input NAND gates to build 4x1 muxes as shown in figure 1.
2. Building 4x1 mux directly from NAND gates: The logical equation of a 4x1 multiplexer is given as:
Now, using De-morgan's law (m + n = (m'n')')
The above equation turns into,
1. Using structural approach: As we know that a 4x1 mux can be structurally built from 2x1 muxes as shown in figure 1 below. Thus, in the same way, we can arrange the 2-input NAND gates to build 4x1 muxes as shown in figure 1.
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| Figure 1: 4x1 mux using NAND gates with structural approach |
2. Building 4x1 mux directly from NAND gates: The logical equation of a 4x1 multiplexer is given as:
Y = (S1' S0' A + S1' S0 B + S1 S0' C + S1 S0 D)where S1 and S0 are the selects of the multiplexer and A, B, C and D are the multiplexer inputs.
Now, using De-morgan's law (m + n = (m'n')')
The above equation turns into,
Y = ((S1' S0' A)' (S1' S0 B)' (S1 S0' C)' (S1 S0 D)')'In other words,
Y = NAND (NAND(S1',S0',A),NAND(S1',S0,B),NAND(S1,S0',C),NAND(S1,S0,D))Thus, we require four 3-input NAND gates and a 4-input NAND gate to implement a 4x1 mux. The implementation is shown in figure 2 below.
