Is there a way to find a logic gate or how to make a more complex gate / bit operator from a wanted truth table I wish to have this truth table :
0 0 = 1
0 1 = 1
1 0 = 0
1 1 = 1
There is a formal way of doing this if you cannot see it from the table.
Write the sum of products
expression for the table.
If 0 0 = 1
, then A'B' is in the expression.
If 0 1 = 1
, then A'B is in the expression.
If 1 1 = 1
, then AB is in the expression.
Then, F = A'B' + A'B + AB
Now, simplify the expression:
F = A'B' + A'B + AB
F = A'(B'+B) + AB Distribution Law
F = A'(1) + AB Complement Law
F = A' + AB Identity Law
F = A'(B + 1) + AB Annulment Law
F = A'B + A' + AB Distribution Law
F = (A' + A)B + A' Distribution Law
F = (1)B + A' Complement Law
F = B + A' Identity Law
It is not(A) or B
.
You have to use a not
gate and an or
gate.
As pointed out in the comments, you can come up from the negated
version of the function.
If 1 0 = 0
, then F' = AB'
Simply, F = not(A and not(B))
. If you distribute the not
, then it will correspond to the same boolean expression as above.
Thanks to the comments for pointing out the shorter way.