Have to make equation with given equation

My instructions was to make a truth table. The inputs was two, 2 binary inputs. With that i had to make an equation. What would be the equation? The teacher said it has something to do with product of sums.

 

Do you have the truth table and need to derive an equation or do you have the equation and need to make a truth table? Sum of products means that the circuit with be an And-Or logic function. It will look something like this: AB + BC + CD. The first level will be a bunch of AND gates. The second level will be 1 OR gate and the input to this OR gate will the output of all the AND gates.

 

it has 4 inputs A B C D and they start from 0000 and goes up to 1111 in binary (16 inputs) and there is 3 outputs x y z and the to get the out puts you would add the binary of A B with C D

 

So the output of the circuit will be A + B + C + D? In this case, the best method might be to make a truth table with all the inputs then fill in the outputs for each line. 16 outputs isn't that bad. To come up with a simplified equation, you can use a K-map which is pretty easy for a 4 variable function. You will need to do 4 K-Maps. You can also try to guess the solution if you know how to build an adder.

 

can you tell me the equation i dont know what that k map is. i have not learned that yet.

i uploaded the truth table i started

 

You need to do AB + CD. The easiest way to do this is to use adders, if you don't know what that is then look it up via the web or your text book. Basically you do B + D. You will get a carry bit. Then you will have to do A+C+Carry Bit. You might get another carry bit. So your output will be MSB Cout S1 S0 LSB. I could give you the equation but you wouldn't really learn anything if I did that.