Question

Given the function f = x(y + w'z) + wxz.

- Show a truth table for the functions.

- Draw a block diagram of a circuit.

- Simplify the circuit using Boolean Algebra or K-Map.

- Re-draw the simplified circuit diagram next to the original circuit.

I NEED HELP WITH THIS ONE. THE IMPORTANT PART IS TRUTH TABLE. IF YOU DON'T KNOW OR DON'T WANT TO DRAW A BLOCK DIAGRAM, IT'S FINE. I NEED TRUTH TABLES FOR THE FUNCTION AND THE SIMPLIFIED FUNCTION. THANK YOU SO MUCH

Answer 1

a)Truth Table

w	x	y	z	w’	w’z	xz	wxz	y+w’z	x(y+w’z)	f = x(y+w’z) + wxz
0	0	0	0	1	0	0	0	0	0	0
0	0	0	1	1	1	0	0	1	0	0
0	0	1	0	1	0	0	0	1	0	0
0	0	1	1	1	1	0	0	1	0	0
0	1	0	0	1	0	0	0	0	0	0
0	1	0	1	1	1	1	0	1	0	0
0	1	1	0	1	0	0	0	1	1	1
0	1	1	1	1	1	1	0	1	1	1
1	0	0	0	0	0	0	0	0	0	0
1	0	0	1	0	0	0	0	0	0	0
1	0	1	0	0	0	0	0	1	0	0
1	0	1	1	0	0	0	0	1	0	0
1	1	0	0	0	0	0	0	0	0	0
1	1	0	1	0	0	1	1	0	0	1
1	1	1	0	0	0	0	0	1	1	1
1	1	1	1	0	0	1	1	1	1	1

Explanation:
Negation(¬) of any logical Identity P is Nothing but Opposite Truth Value for P. i.e If P is T then (¬P) is F

And gate is used to find the Product of Two literals P AND Gate Q Output is PQ is T if and only if both P and Q are T else PQ is F

OR gate is used to find the Sum of Two literals P OR Gate Q Output is P+Q  is T if and on if any one of P and Q are T else P+Q is F

3) From the above truth table

Given Function is

f (w, x, y, z) = ​ m (6, 7, 13, 14, 15)

Above Function in K-map as follows

Simplified K-map as follows

The Simplified SOP of f (w, x, y, z) = wxz+xy

Simplified Circuit:

Given f (w, x, y, z) = wxz+xy

Explanation:
Negation(¬) of any logical Identity P is Nothing but Opposite Truth Value for P. i.e If P is T then (¬P) is F
And gate is used to find the Product of Two literals P AND Gate Q Output is PQ
OR gate is used to find the Sum of Two literals P OR Gate Q Output is P+Q