# Making a 4 x 16 decoder with 2 3 x 8 decoders

Discussion in 'Homework Help' started by jjacq13, Sep 26, 2011.

1. ### jjacq13 Thread Starter New Member

Sep 26, 2011
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0
Can anyone show me how to make a 4 x 16 decoder from 2 3 x 8 decoders. I need very basic info (truth tables and basic gates). Thanks, any and all info is appreciated. If you could explain what the output of the gate is that would be helpful too.

2. ### Zazoo Member

Jul 27, 2011
114
43
Can you show some of your initial work?

One hint: You'll need to use the enable lines for the 3x8 decoders.

3. ### jjacq13 Thread Starter New Member

Sep 26, 2011
5
0
Basically I have x,y, and z outputting to C (Carry) and S (Sum)

x y z | C S
0 0 0 | 0 0
0 0 1 | 0 1
0 1 0 | 0 1
0 1 1 | 1 0
1 0 0 | 0 1
1 0 1 | 1 0
1 1 0 | 1 0
1 1 1 | 1 1

C(x y z) = Ʃ(3,5,6,7)
S(x y z) = Ʃ(1,2,4,7)

Does that help? As you might guess, I'm kind of lost. I am wondering what the ouput table is for the 4 x 16, what it is decoding.

4. ### Zazoo Member

Jul 27, 2011
114
43
Perhaps I'm confused. These appear to be two separate problems.

The first is using two 3-to-8 encoders to mimic a single 4-to-16 encoder.
The second is, I'm guessing, how to mimic a full-adder using a 3-to-8 decoders (and gates)?

What's the exact problem you are working on?

5. ### jjacq13 Thread Starter New Member

Sep 26, 2011
5
0
It is the first (two 3-to-8 encoders to mimic a single 4-to-16 encoder). It's just that I'm having trouble understanding what's really going on. Thanks for your help.

6. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Think about it as selecting between two identical selection gizmos. First you must select which one you want to operate and then you give it the info it needs.

More specifically: Your input is 4 bits long. The addresses 0XXX will refer to the first decoder and the addresses 1XXX to the second. That means that the three LSBs will be common to the two decoders and the difference will be made by the MSB.
This is where the Enable input of the decoders will come to play.

Can you take it from here? Can you make an effort and post it?

7. ### jjacq13 Thread Starter New Member

Sep 26, 2011
5
0
So the MSD dictates the 3 x 8 decoder that is giving the output, (0 for 3 x 8 # 1, 1 for 3 x 8 #2) giving 16 outputs (8 from each 3x8). What is the meaning of the decoder. what is it decoding. What is the logic? As I said in an earlier post, the 3x8 we made in class was a Carry-Sum decoder, what is the 4x16 doing. Thanks for your help.

8. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Decoders have variable uses.
If you would like to select one device amongst 16 attached to a data bus, it wouldn't be practical to have 16 on/off bits to drive them. With only 4 bits you can name the device in binary and the decoder will select the correct device.
For the purpose mentioned in your classroom, a 3-to-8 decoder can help you implement a 3-variable Boolean function. A 4-to-16 decoder is suitable for a 4-variable function.

In the end, a decoder is merely a device to which you tell a number in binary and it selects the corresponding output (1st, 2nd, etc).

Is that clear?

Last edited: Sep 26, 2011
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9. ### jjacq13 Thread Starter New Member

Sep 26, 2011
5
0
Yes, thanks a lot you've been very helpful.