Hi everyone,

I have this assignment with Boolean algebra and logical gates. Because I'm not in an English speaking country I will try my best to translate it from my native language. Sorry if I make any mistake and if you need more info please reply.


Assignment :
If we have four variables x,y,z,d and are divided in pairs. x and y in group A and z, d in group B. Find the function that defines A = B ( A is equivalent to B). When you find the function draw logical circuit that is based on that function

Description :
This assignment is based on truth table. Group A and group B are equivalent when variables in group A (x,y) are for example 0 1 and variables in group B(z,d) are 0 1. But they aren't equivalent when for example group A is 1 1 and group B 1 0

What I need is how can I define this function. If someone helps me to find it, I don't think drawing logical circuit is hard based on that function.

Thanks in advance.

 

I think first, that you need to define a column in your truth table that represents "equivalence". Then, look at the truth table and see if all combinations are represented. For example on your post, there is no row that represents xy = 00 and zd = 10

 

You have four inputs, so your truth table should have 2^4, or 16, rows. This allows you to then specify the output of your logic function for every possible combination of the inputs. You have only identified the four combinations for which the output should be True. As long as you annotate the table with something like "All others" for the inputs and "False" for the output, that will suffice.

If you have a box with a bunch of two-input AND, OR, XOR, NAND, NOR, XNOR plus NOT gates, then you can implement this circuit using just three gates from the box, two of which are the same type. That gives you a benchmark to sanity check your solution against.

 

Thanks for your replies and correcting me. Problem is that since you replied I'm trying different combinations but non of them seams to work based on truth table. Is there a formula in which I can find the solution or should I try and try until I find it. Or there isn't any solution at all!

 

Do the blue check marks indicate when you WANT the output to be True? Or when is IS True based on your circuit?

If it's when you WANT the output to be True, why do you have the case A=01, B=10 and the case A=10, B=01 checked?

You give no indication in your schematic of which signal is X, Y, Z, or D.

Please don't make us guess at all of these things. We are not mind readers and our crystal balls don't work worth a damn. When you want free assistance from strangers, you need to put forth the effort to make it easy for them to see what you are thinking and doing. Otherwise they will just find some better way to spend their time.

Where did your function (x+y)(z+d) come from? What is your thinking behind it?

Given your stated goal, that you want the output to be high when A equals B, phrase that statement in terms of logic concepts, such and AND, OR, NOT and so forth.

Here's a start:

1) The output should be HI when A and B are equal.
2) A and B are equal when (something involving x and z) AND (something involving y and d).

Rewrite the phrases in parentheses along the lines of the first statement and then write statements 3 and 4 to have a similar relationship to those phrases that statement 2 has to statement 1.

 

Take a look at the rows 1001 and 0110

I don't think they should be checked. Also, instead of checks, make a column with 1s in place of the checks and 0s elsewhere.