Logic Simulation 1

ECE-C211
Simulation 1
Boolean Algebra - Theory And Application

Prove that [ X + X' = 1 ]

Truth Table for [X+X']
X	X'	f(X)
0	1	1
1	0	1

top: (X+X') at X = 1 lower: (X+X') at X = 0
[top: (X+X') at X = 1 lower: (X+X') at X = 0]

As you can see the two simulations above produce equal results even though they are both implimented differently. This is due to the fact that whenever you have a variable and it's complement OR'ed it will always produce one... if either one is zero its complement is one and so the statement is true. If either one is "1" then it automatically makes the statement true!

Prove that ( X + YZ = (X+Y)(X+Z))

Proof of X+YZ = (X+Y)(X+Z)
X	Y	Z	X+YZ	(X+Y)(X+Z)
0	0	0	0	0
0	0	1	0	0
0	1	0	0	0
0	1	1	1	1
1	0	0	1	1
1	0	1	1	1
1	1	0	1	1
1	1	1	1	1

Let us demostrate via a simulation:

First [X+YZ]: [X+YZ Simulation]

Second [(X+Y)(X+Z)]: [(X+Y)(X+Z) Simulation]
As you can see in the above images... again the implimentation from the previous diagram is different but it still complies with the truth table.

polywog@drexel.edu next previous