Designing a 16x1 Multiplexer Using 8x1 MUX and NAND Gates

How can you create a 16x1 MUX using only 8x1 MUX and NAND gates?

Is it possible to design a 16x1 MUX with a combination of 8x1 MUXs and NAND gates?

Answer:

To create a 16x1 MUX using 8x1 MUXs and NAND gates, connect two 8x1 MUXs' inputs to the respective data lines, their selection lines in parallel, and use the most significant bit with a NAND gate for enable lines. Outputs of both MUXs are then connected through another NAND gate to get the final output.

To design a 16x1 MUX using only two 8x1 MUX and NAND gates, we can utilize the fact that a 16x1 MUX can be considered as two 8x1 MUX with an additional selection line. Given that an 8x1 MUX has 3 selection lines, the 16x1 MUX will have 4 selection lines. The most significant selection line (let's call it S3) will determine which 8x1 MUX will pass its data to the output.

Here's the design approach:

• Take two 8x1 MUX devices. Each 8x1 MUX has 8 inputs, 3 selection lines, and 1 output.
• Connect the inputs of the two MUX devices to the 16 data input lines you wish to have on your final 16x1 MUX.
• Connect the selection lines S0, S1, and S2 of both 8x1 MUX devices in parallel. These will be the least significant bits of the selection inputs on your 16x1 MUX.
• Take the most significant selection line S3 and connect it to a NAND gate. The other input of the NAND gate will be connected to the enable inputs (active low) of both 8x1 MUX devices.
• The output of the NAND gate will be connected to the enable input of one of the 8x1 MUX devices, while the S3 line itself will be connected to the enable input of the other 8x1 MUX directly.
• The outputs of the two 8x1 MUX devices will then be connected to a NAND gate, where the output of this NAND gate will be the final output of your 16x1 MUX.