Logic gate circuit for 3 inputs (A, B, C) with custom output truth table

Does anyone know how to design a system with logic gates with 3 choices, A, B and C, having the following logic?:

A B C OUTPUT
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0

I am thinking of using two XOR gates. but how can i do it by using only one on-off switch (for only two inputs)?

Well, I am not sure of on-off switch, but this can be implemented with a single 4X1 mux with control pins set to B, C and inputs as A, not(A), not(A), 0.

Well I hope you have herd of Karnaugh maps, simplistic way to determine minimum number of gates to realize a function. Although you could do the product of sums or sums of products and then reduce it.

Example:

(Anot & Bnot & C)*(Anot & B & Cnot)*(A & Bnot & Cnot)= Output, this is no guarantee that it represents the minimum number of gates, alternate you could do the same for; = Output_not.

So in this example all three inputs need an inverter (three inverters) and three input AND gates. Now I just did this off the top of my head, the best way is to finish the product of sums which I have started or use the Karnaugh map technique which is super easy and does not involve (little) Boolean Logic skills. This is like Freshman/Sophomore college stuff.

http://en.wikipedia.org/wiki/Karnaugh_map

Oh I forgot to mention, you would need one - 3-input OR gate to produce an output from the and gates. Sorry for the exclusion.

thank you for your help!

anyway, do you know of any free softwares that i can use to draw circuits on Mac?

Here is a solution to your problem Elsie,
I hope you know how to draw K-maps for three inputs, draw it & you will get an expression in the form
y= a+~ab~c (~ indicates inverted form of the input)
Therefore you need to use 2 NOT gate, 2 AND gate & 1 OR gate for this logic!
I have attached a picture of what i have drawn, Hope it helps!

There is software called logicalcircuit www.LogicCircuit.org but Im not sure if they have a mac version

Ps just looking at your question why dont you just simply use a micro chip 3 inputs and implement a lookuptable or do they want discreet circuitry

Just far easier thats all plus of course they dont do this anymore its so out of date with respect to modern methods of achieving the same with just one component

Thats the good part about microchip If I want a 4017 I write software for a 16F88 and ive got one
If I want a 4 input Nand gate I wrote software same chip and I have one
If I want a. Decimal to Bcd encoder I write software bingo ive got one simply using same chip all the time

If I want serial to parrellel convertor bingo write software for same chip and Ive got one

See the advantages now

Why use 5 different chips when all I have to is write software for one single chip a couple of input pins or even one pin for that matter and bingo Ive git 4, 5,6,10 different ttl version gates all in one chip or any user defined logic state or sequence and whats difficult about it

A bit of boolean algebra and away you go or predicate calculus which isnt that difficult

Plus efficiancy, cheap, cost effective, re usable, selectable, change functionality in realtime

Got to be better hasnt it I dont realy understand why they dont teach you this right from the word go

Just makes more sense!

You should point this out to instructors This is what Industry demands now and it prepares you for FPGA and future employment

No point in fighting against this You move with it All heading this way now what with digital audio mobile phones any industrial appliance, even power supplies, buck convertors, motor controll, light dimmers, cars security automated cash points, banks you name it all FPGA or microchip plus of course, operating conditions sleep functions, energy efficiant and green compliant

Except Japs and chinese who like the blob on the pcb which you cant replace bit stupid but some international negotiation required to get them to see sense in preserving and creating reusable components

Not to worry Im sure they will see reason in preservation soon enough

Mark H

Yes but the principals still apply be it in hardware or software. I was thinking this looks very similar to a test question where you don't have options of simple programable logic arrays.

Very good, reduction of the product of sums.

Thanks for your help! But I was thinking about just using 2 XOR gates, because I have only toggle switch to use.. See attached if I'm correct.

Aah yes you still have to learn principles Agree that will never change just the method that we use changes as does the tools

No arguments what so ever their at all

Practical however should include but with not as emphasis as much of this can be achieved by reatime simulators i.e the software link ive just placed in previous comments, also longterm more economical than real hardware though i would add that although simulators are available, not everything you do on pc works in the real enviroment as im sure they will find out too

Hi elsie

How many broken dumped microwaves,alarm clocks, dvds,cd players etc do you see Loads

Suggestion take one apart and low and behold as many switches as you want That is how i make my projects all the time from scrap and cpu well look on ebay so cheap I dont even go into maplins etc Unless i apsolutley have to now

0.25 PENCE FOR ONE RESISTOR From Maplins OR 5000 FOR UNDER £20.00
Andon 5000 they still manage to donate to charitable causes Thats 0.004 pence for one resistor and they still manage to pay staff decent wages and thier attitude is always pleasant unlike quite a few others whos names I shall not utter at the moment

Come on think even I think thats wrong Its a disgusting price from these so called big players You know I know this too


The amount of dumped electrical goods is shockingly high Got to be a use for them hasent there

Do you see, Elsie, where your XOR implementation is ALMOST good enough? The problem is, when A and B are both HI their XOR output will be LO, and then a HI C will propagate as HI through the following XOR. So 111 will end up 1, not 0, unfortunately.

Of all the solutions proposed the MUX is best: lowest chip count, less wiring. Multiplexors (aka Data Selectors) are powerful!

I have to admit I don't quite understand how the toggle switch is supposed to be used. Will the switch always be putting a LO on one input, a HI on another, while the third input is some outside signal you are trying to gate? I'm very unclear on the switch part, obviously...

I don't think you will be able to implement your logic using only 2 xor gates.
The result i have provided to you is a standard one. Implementing it using xor will be difficult & may not work.

Only one way he can use a toggle switch with on or off thats as clock source which means he would have to provide a counter which counts to 7 bin "0111"and then decode the counter to show state i.e 111, 110, 101,100 etc and then move this to his appropriate output

Almost FPGA in essence So his first part would be to create a binary counter circuit capable of counting to dec 7 Thats the first part by the looks of this

IF we look at the decimal ouput im looking for a pattern here I can see, 3,2,1 but no set pattern after this to see if there is some type of number sequence there doesent appear to be one

His dec output is
0,3,5,6,9,12,14
n+3, n+2,n+1 THEN NO PATTERN unless someone else can see something here that im missing

I think we have part of this for you create a 3 stage binary counter then use the diagram provided by Syed now you only have to use the toggle switch to count to 7 You would have to clock your state in for the input using leds to indicate state of switches then couple the output using Syeds diagram

Ive just read that article Syed, interesting perhaps you can show us how to use this for 3 inputs I understood single input but cant see how you use 3 inputs Perhaps you could do a write up on this showing how this is done

See attached

I believe we're going around in circles here. There's still no clarity about the application of the toggle switch.

It may be for clocking, in which case Mark's counter will serve as a front end, and either Satyanarayana's MUX solution or Syed's minimization can then decode the counter's output.

But Elsie's description and diagram don't specify whether the toggle is a clock, or an input, or ... ?

And I think Elsie has abandoned the conversation. ;^)

I think the questions are being asked deliberately to assertain what peope dont know as opposed to what they do know Although they do seem a little sneaky here but correct in evaluating how to stimulate thought in the direction of progressing towards FPGA designing your own own ALU and MUX geared towards cpu design combined

I notice with other questions by elsie regarding maths, c, matrice theory, bit manubulation and Image reduction, graphics 2g which in turn teaches or moves towards ieee formats for long number, floating point numbers and thier representation and maths for multiplication, division etc

Thought provoking definately they are too but clever in context as this sound like final year projects involving hardware for computer systems organisation at computer science degree level

Obviously to develop LCD COLOUR GRAPHICS in vehicles and electronic. ,electrical switches using gui design principles involving embedded technology, smart cards, with can bus architecture, i2C bus and with RF networking including bluetooth and web technogies lcd tv etc