8-line to-256-line decoder using 4-line to-16-line decoders is shown below

Explanation:

To understand why the correct answer is option B, let's break down the problem step by step.

1. Understanding the problem:

We need to design an 8-line-to-256 line decoder. This means that we have 8 input lines and 256 output lines. Each input combination should activate a single output line.

2. Understanding the decoder:

A decoder is a combinational logic circuit that converts binary input codes into output lines. In this case, we need to design a decoder that takes an 8-bit binary input and activates one of the 256 output lines based on the input combination.

3. Understanding the 4-line to-16 line decoder:

A 4-line-to-16 line decoder is a decoder that takes a 4-bit binary input and activates one of the 16 output lines based on the input combination. It has 4 input lines and 16 output lines.

4. Designing the 8-line-to-256 line decoder:

To design an 8-line-to-256 line decoder, we can use a hierarchical approach by combining multiple 4-line-to-16 line decoders.

Since each 4-line-to-16 line decoder has 4 input lines and 16 output lines, we can use two 4-line-to-16 line decoders to cover 8 input lines. This will give us 32 output lines (16 from each decoder).

5. Expanding to cover all 256 output lines:

To cover all 256 output lines, we can cascade multiple sets of the two 4-line-to-16 line decoders. Each set will provide an additional 32 output lines.

The number of sets required can be calculated by dividing the total number of output lines (256) by the number of output lines per set (32).

256 / 32 = 8

So, we need 8 sets of the two 4-line-to-16 line decoders to cover all 256 output lines.

6. Calculating the total number of decoders required:

Since each set consists of two 4-line-to-16 line decoders, we can calculate the total number of decoders required by multiplying the number of sets by the number of decoders per set.

8 sets * 2 decoders per set = 16 decoders

Therefore, the correct answer is option B, 17 decoders are required to make an 8-line-to-256 line decoder.

Summary:

To create an 8-line-to-256 line decoder, we can use a hierarchical approach by combining multiple 4-line-to-16 line decoders. By cascading 8 sets of the two 4-line-to-16 line decoders, we can cover all 256 output lines. Hence, the correct answer is option B, 17 decoders are required.