5 to 24 decoder from 3 to 8 decoders

[spingk]

Homework Statement

Design a 5:24 decoder using three 3:8 decoders and one 2:4 decoder.
1)Show the truth table.
2)Draw a block diagram of the final decoder. Use X4 as the MSB and X0 as the LSB.

2. The attempt at a solution
I have the truth table drawn. Because it is a 33 line truth table I don't want to type it out. But I start out with:
EN X:43210 Y:
0 xxxxx
1 00000 Y0=1
1 00001 Y1=1
...
1 10111 Y23=1

I am having trouble figuring out how to connect the decoders to get a proper decoder.

 

[Valkarie]

In the past we have drawn out the circuit diagrams with gates, but this seems to be slightly different. Could I get some help on how to draw the block diagram?

 

[Mene]

I would first start by reviewing the basics of decoders and their functions. A decoder is a digital circuit that converts coded inputs into coded outputs according to a specified logic function. It essentially takes a binary input and activates a specific output line based on the input code.

In this case, we are asked to design a 5:24 decoder using three 3:8 decoders and one 2:4 decoder. This means we need to take a 5-bit binary input and produce a 24-bit output. This can be achieved by using three 3:8 decoders, each with 3 input lines and 8 output lines, and one 2:4 decoder with 2 input lines and 4 output lines.

To start, we can label the three 3:8 decoders as A, B, and C, and the 2:4 decoder as D. The inputs to the decoder will be labelled as X4, X3, X2, X1, and X0, with X4 being the most significant bit (MSB) and X0 being the least significant bit (LSB). The outputs of the decoder will be labelled as Y23, Y22, Y21, ..., Y1, Y0, with Y23 being the most significant bit (MSB) and Y0 being the least significant bit (LSB).

To create the truth table, we need to consider all possible input combinations for the 5-bit binary code. This means we will have 32 rows in our truth table, with each row representing a different input combination. The outputs for each row can be determined by the following logic function:

Y23 = A0 * B0 * C0 * D0
Y22 = A0 * B0 * C0 * D1
Y21 = A0 * B0 * C1 * D0
Y20 = A0 * B0 * C1 * D1
Y19 = A0 * B1 * C0 * D0
Y18 = A0 * B1 * C0 * D1
Y17 = A0 * B1 * C1 * D0
Y16 = A0 * B1 * C1 * D1
Y15 = A1 * B0 * C0 * D0
Y14 = A1 * B0 * C0 * D1
Y13 = A1 * B0 *