How Can You Build an 8-Input Multiplexor with a 3-Input Decoder and NAND Gates?

[cranincu]

Homework Statement

The question is to:

Implement an eight-input multiplexor using a three-input decoder and NAND gates

The Attempt at a Solution

Not sure how to work this at all. The decoder has 3 inputs and the multiplexor has 8. So if the selectors of the Multiplexor are 101 that implies that it outputs x_5, but how can you get x_5 out of a decoder and some NAND gates?

edit: Oh wow, nevermind. Was about to go to sleep then it just hit me like lightning to figure it out. the decoder's the selects and goes into nand gates which are fed x_0 to x_7, that's ridiculously easy

 

[KataKoniK]

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Hi there,

Thank you for your post. I am a scientist and I would be happy to help you with this problem.

To implement an eight-input multiplexor using a three-input decoder and NAND gates, we can follow these steps:

1. First, let's label the inputs of the multiplexor as x0, x1, x2, x3, x4, x5, x6, and x7.

2. We will also label the three inputs of the decoder as A, B, and C. These inputs will act as the selectors for the multiplexor.

3. Now, we need to create a truth table for the multiplexor. This will help us understand the behavior of the multiplexor and how the inputs and selectors are related.

4. The truth table will have 8 rows (representing the 8 possible combinations of inputs) and 3 columns (representing the 3 selectors). The output of the multiplexor will be a single column, representing the selected output.

5. Now, let's look at the truth table of a 3-input decoder. It has 8 rows (representing the 8 possible combinations of inputs) and 3 columns (representing the 3 inputs). The output of the decoder will be a single column, representing the selected output.

6. We can see that the truth tables of the multiplexor and the decoder have the same number of rows and columns. This means that we can use the output of the decoder as the selectors for the multiplexor.

7. We will use the outputs of the decoder (A, B, and C) as inputs for the NAND gates. These NAND gates will be connected to the inputs of the multiplexor (x0 to x7). The output of each NAND gate will be connected to the corresponding input of the multiplexor.

8. Now, when we give a specific combination of inputs (x0 to x7) and selectors (A, B, and C), the multiplexor will select the output from one of the inputs and pass it on as the output.

I hope this helps you understand how to implement an eight-input multiplexor using a three-input decoder and NAND gates. Please let me know if you have any further questions. Good luck!

 

[Mene]

I would approach this problem by first understanding the basic principles of a multiplexor and a decoder. A multiplexor is a digital circuit that selects one of several inputs and outputs it based on a control signal. A decoder, on the other hand, is a digital circuit that converts an n-bit input into 2^n output lines, with only one output line being active at a time.

In this scenario, we are asked to implement an eight-input multiplexor using a three-input decoder and NAND gates. This means that we need to use the decoder to generate the control signals for the multiplexor and use NAND gates to select the appropriate input.

To begin, we can use the three inputs of the decoder to generate 2^3 = 8 output lines. These output lines will act as the control signals for the multiplexor. We can then use NAND gates to select the appropriate input based on the control signals.

For example, if the control signals are 101, we can use NAND gates to select input x_5 and output it as the final output of the multiplexor. This can be done by connecting the three control signals to the inputs of the NAND gates and connecting the outputs of the NAND gates to the inputs of the multiplexor. This way, the selected input will be passed through the NAND gates and outputted by the multiplexor.

In conclusion, by using the decoder and NAND gates, we can implement an eight-input multiplexor with ease. This approach not only simplifies the design process but also makes the circuit more efficient and compact. it is important to understand the fundamental concepts behind these digital circuits in order to effectively implement them in various applications.