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Mux exercise. Is it right?

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Romadness

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Logic Gates with MUX: 2 XOR, 1AND

Can someone help me ?

I should convert this function (A XOR B) AND (C XOR B) in a mux circuit.

JjiWyqC.png
 

Re: Logic Gates with MUX: 2 XOR, 1AND

Hi,

you may use a K-map...

Three inputs may be the control_inputs to a MUX.
Now you just have to do the correct fix_level to each signal_input.

Start drawing with a table which shows every different possible control_state.
Then fill the table with the expected output levels.
Then draw a schematic with the information from the table.

***
Indeed it´s very simple, but it makes no sense to give you the ready solution. For sure you don´t expect this.

Klaus
 
Re: Logic Gates with MUX: 2 XOR, 1AND

I can't continue:

WU7MJWh.png
 
Last edited by a moderator:

Re: Logic Gates with MUX: 2 XOR, 1AND

Pick one of the signals and make it a mux select...hopefully you know what a 2:1 mux circuit does...

Look at the truth table, there is a somewhat obvious choice of which input should be used as the mux select.
 

Re: Logic Gates with MUX: 2 XOR, 1AND

I know how 2:1 mux work, but i missed one lesson. I don't know how convert an circuit into mux
 

Re: Logic Gates with MUX: 2 XOR, 1AND

I know how 2:1 mux work, but i missed one lesson. I don't know how convert an circuit into mux
It seems to me you may know how it works but don't know what the circuit looks like. i.e. the boolean equation.

Do a google search for "mux boolean expression" and that should help.
 

I have this function (A XOR C ) AND ( A OR B ) I have to turn it into 2:1 MUX. I did in this way:

8uovDutg.png

I did right?


P.S. Sorry for my english. I'm learning it
 

does the problem expect you to use a 2:1 mux as an inverter?

--edit:

you have s0/s1 which are not generated using muxes.
 
Last edited:

does the problem expect you to use a 2:1 mux as an inverter?

does the problem expect an optimal solution? eg, one that allows a/b/c to be mux inputs?

Exercise says: Using only 2: 1 multiplexers and input signals, A,B,C,NOTA,NOTB,NOTC,0,1, draw a circuit equivalent to the Boolean expression (A XOR C) AND (A OR B).
 

First, a 2:1 mux can create an inverter, an and-gate, and an or-gate. Even without effort, you could construct the mux circuit based on replacing and/or/invert with the mux2 version. You can prove this to yourself by applying 1/0 to one of the mux inputs, a0 to the other input, and a1 to the select. There are four possible cases, so you can quickly determine which one is whcih. I'm using a0/a1 as the variable name has nothing to do with a/b/c from the problem. Just that you can get a0 and a1, a0 or a1, as well as !a0.

This problem probably doesn't want you to do this. It probably wants you to notice that there are only two cases where there is a 1 output. from there that both expressions use the same inputs, but with opposing polarity. This should suggest choosing one input as a select. Then use the above and/or conversion for both mux input cases.
 
First, a 2:1 mux can create an inverter, an and-gate, and an or-gate. Even without effort, you could construct the mux circuit based on replacing and/or/invert with the mux2 version. You can prove this to yourself by applying 1/0 to one of the mux inputs, a0 to the other input, and a1 to the select. There are four possible cases, so you can quickly determine which one is whcih. I'm using a0/a1 as the variable name has nothing to do with a/b/c from the problem. Just that you can get a0 and a1, a0 or a1, as well as !a0.

This problem probably doesn't want you to do this. It probably wants you to notice that there are only two cases where there is a 1 output. from there that both expressions use the same inputs, but with opposing polarity. This should suggest choosing one input as a select. Then use the above and/or conversion for both mux input cases.

then i did it in this way:

Qw8dmk6.png

Is it right?
 

(Sorry fir the confused order)

Hi,

Never leave an unused input floating.

Klaus

- - - Updated - - -

Hi,

There are many possible solutions.
You said it should be made by MUX. You don't speak of any other logic cifcuit.
Because you have 3 (control) inputs, I'd build a MUX with 3 control inputs.
This is a 1 of 8 MUX.
Then just give to each signal input the fix state you want.

Klaus
 
also, is this "(A xor B) and (B xor C)" or is this "(A xor B) and (B or C)"? I noticed the original problem used xor twice and then the last two used xor and or.
 

It is the second one, At the end is the same exercise. I want understand the logic to solve this kind of problem.
 

In the following description I assume that 'not a' is 'a' ('a' with underline).
I also assume that 'a and b' = 'ab' and 'a or b' = 'a+b'.


First of all you need to transform equations algebraically (you need to know Boolean algebra).
Second you need to know what is the equivalent equation for the mux2:1 (see

https://en.wikipedia.org/wiki/Multiplexer
)
it is:
z=as+bs,

where:
'a' and 'b' are inputs;
's' is a MUX control signal.

then

(a xor b) and (b xor c) =
[(ab)+(ab)]*[(bc)+(bc)] =
ab(bc+bc)+ab(bc+bc) =
abbc+abbc+abbc+abbc =


now:
abbc = 0
abbc = abc
abbc = abc
abbc = 0

so:

(a xor b) and (b xor c) = abc + abc

now use mux2:1 equation:
ab as input 0
ab as input 1
c as MUX control signal. - and draw that MUX

now all you need is to express ab as another mux2:1 and the same for ab (this is a little bit tricky):
ab = ab + '0'b (a as input 1, '0' as input 0, b as MUX control signal) - and draw that MUX
ab = ab + '0'b (a as input 0, '0' as input 1, b as MUX control signal) - and draw that MUX

After all you have 3 MUXes connected together.
Hope that was helpful.
 
Last edited by a moderator:

It is the second one, At the end is the same exercise. I want understand the logic to solve this kind of problem.

it looks correct. I don't like this problem though as it doesn't seem like there is any guidance to solving it. You can solve it by creating an 8:1 mux, or by converting and/or logic, or by noticing better options. I wouldn't put too much effort into this as it doesn't really come up ever again. It basically just trains you on what a mux is.
 

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