Digital Circuit Help: Solve for Truth Table & Boolean Function

[fsm]

Homework Statement

1. Derive the truth table for the circuit.
2. Derive the Boolean function directly from the circuit.

I can't the function to agree with the truth table. I don't know what I'm doing wrong. I somewhat positive my truth table is right, but I think my function statement is wrong.

Homework Equations

None that I know of.

The Attempt at a Solution

1. Rather than show a huge truth table I'll list the sum of products-$$\sum$$(2,6,10,11,12,13,14,15)
2. F=((w(x+y)')(y'+z))'
=(w(x+y)')'(y'+z)'
=(w(x+y))(y'+z)'
=(wx+wy)+y+z'
=wxy'z'+wxyz+wx'yz'+wxyz+w'x'yz'+wxyz+w'x'y'z'+wxyz'
=wxy'z'+wxyz+w'x'yz'+wx'yz'+wxyz'

 

[asd1249jf]

Homework Statement

1. Derive the truth table for the circuit.
2. Derive the Boolean function directly from the circuit.

I can't the function to agree with the truth table. I don't know what I'm doing wrong. I somewhat positive my truth table is right, but I think my function statement is wrong.

Homework Equations

None that I know of.

The Attempt at a Solution

1. Rather than show a huge truth table I'll list the sum of products-$$\sum$$(2,6,10,11,12,13,14,15)
2. F=((w(x+y)')(y'+z))'
=(w(x+y)')'(y'+z)'
=(w(x+y))(y'+z)'
=(wx+wy)+y+z'
=wxy'z'+wxyz+wx'yz'+wxyz+w'x'yz'+wxyz+w'x'y'z'+wxyz'
=wxy'z'+wxyz+w'x'yz'+wx'yz'+wxyz'

Do you know how to do a Karnaugh map? If you can write the truth table for this, that is the easiest way to go about this problem.

 

[fsm]

Yes I can. I'll try that.