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algorithmbit-manipulation

Logic gate whose truth is 1101

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

Solution

  • 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.

    Alternative Solution

    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.