# Representing a demultiplexer-multiplexer circuit with basic gates

#### ogelin

Joined Dec 8, 2015
4

I have been given this circuit, which I'm supposed to represent with only AND, OR and XOR gates. I've written this as my truth table for the circuit:

IN0 | IN1 | OUT
----------------
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

However this would give an NXOR gate, which I'm not allowed to use. I'm thinking I might have messed the truth table up, but I can't see where.

#### crutschow

Joined Mar 14, 2008
26,053
You can make an inverting gate by connecting one input of an XOR gate to logic high.

#### WBahn

Joined Mar 31, 2012
26,398
View attachment 96168
I have been given this circuit, which I'm supposed to represent with only AND, OR and XOR gates. I've written this as my truth table for the circuit:

IN0 | IN1 | OUT
----------------
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

However this would give an NXOR gate, which I'm not allowed to use. I'm thinking I might have messed the truth table up, but I can't see where.
So are you only allowed to use ONE gate? I'm betting you can use any of those gates multiple times, if needed.

Could you do it if they added a NOT gate to the set of allowed gates?

If so, then can you make a NOT gate given those three gates as your parts kit?

#### ogelin

Joined Dec 8, 2015
4
So are you only allowed to use ONE gate? I'm betting you can use any of those gates multiple times, if needed.

Could you do it if they added a NOT gate to the set of allowed gates?

If so, then can you make a NOT gate given those three gates as your parts kit?
Yes, I can use them multiple times, as needed. I need a NOT gate, but I don't think I can make one from what they've given. Can I?

#### WBahn

Joined Mar 31, 2012
26,398
Yes, I can use them multiple times, as needed. I need a NOT gate, but I don't think I can make one from what they've given. Can I?
Consider that a NOT gate has one input while all of the gates you have available to you are two input. But there is nothing that prevents you from using one of the two inputs for your signal and just tying the other signal either HI or LO. If you do that, how do the various gates behave? Does one of them behave like a NOT gate?

#### ogelin

Joined Dec 8, 2015
4
Consider that a NOT gate has one input while all of the gates you have available to you are two input. But there is nothing that prevents you from using one of the two inputs for your signal and just tying the other signal either HI or LO. If you do that, how do the various gates behave? Does one of them behave like a NOT gate?
But wouldn't I need a NOT gate to make it LO?

#### WBahn

Joined Mar 31, 2012
26,398
But wouldn't I need a NOT gate to make it LO?
Why?

Where is the HI coming from that you would be feeding into the NOT gate? If you have this HI available, why wouldn't you also have a LO available?

Where are the HI and LO coming from that you are applying to IN0 and IN1? If you have those available to use for those inputs, why wouldn't you have them available in general?

You can generally assume that you have static HI and LO always available to you. In physical systems these are just the logic power supply rails.

#### crutschow

Joined Mar 14, 2008
26,053
Yes, I can use them multiple times, as needed. I need a NOT gate, but I don't think I can make one from what they've given. Can I?
You missed my post #2.

#### hp1729

Joined Nov 23, 2015
2,304
View attachment 96168
I have been given this circuit, which I'm supposed to represent with only AND, OR and XOR gates. I've written this as my truth table for the circuit:

IN0 | IN1 | OUT
----------------
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

However this would give an NXOR gate, which I'm not allowed to use. I'm thinking I might have messed the truth table up, but I can't see where.
Your truth table looks right. On the decoder if the IN0 input is "0" the "0" output is high. If the IN0 input is "1" the "1" output is high. The Select line routes the chosen line to the output.
I think one lesson here is how to get an inverter.

Last edited:

#### sailorjoe

Joined Jun 4, 2013
363
Ogelin, your first post has almost all the information you need. Your truth table is correct and your conclusion of it being a NXOR gate is also correct. The other posters have given you what you need. From your responses it appears to me that you're missing what they're telling you because you believe the given circuit has all the things you need. But there is something available to you not shown on the diagram, and that is a fixed logic HI and a fixed logic LO. These are like constants you can use any time. In a physical circuit we get a logic HI by connecting a gate input to a high voltage (possibly through a resistor), and we get a logic LO by connecting an input to ground. You're dealing with logic and not with voltages, so you can just create a logic HI where you need it by labeling a gate input as HI or LO.

By the way, we generally never connect our logic gate outputs to either HI or LO because that would defeat the purpose of the logic gate, and sometimes fries our circuits.