2) Logical Operations Flashcards
Needed operations
NOT, AND, OR, XOR
NOT
Only one input and output.
Reverses input
A Q
1 0
0 1
AND
Has 2 inputs and 1 output
Both inputs must = 1
A B Q 0 0 0 0 1 0 1 0 0 1 1 1
OR
Has 2 inputs and 1 output
1 input must = 1
A B Q 0 0 0 0 1 1 1 0 1 1 1 1
XOR
Has 2 inputs and 1 output
output is only 1 is A and B are different
A B Q 0 0 0 0 1 1 1 0 1 1 1 0
Annulment Law
A.0 = 0
A + 1 = 1
Identity Law
A + 0 = A
A.1 = A
Idempotent Law
A + A = A
A.A = A
Complement Law
A.Ā = 0
A + Ā = 1
Commutative Law
A.B = B.A
A + B = B + A
Double Complement Law
𝐴̿ = A
Distributive Law
A(B + C) = A.B + A.C
A + (B.C) = (A + B).(A + C)
Absorptive Law
A + (A.B) = A
A(A +B) = A
Associative Law
A + (B + C) = (A + B) + C = A + B + C
A(B.C) = (A.B)C = A.B.C
A.0 = 0
A + 1 = 1
Annulment Law
A + 0 = A
A.1 = A
Identity Law
A + A = A
A.A = A
Idempotent Law
A.Ā = 0
A + Ā = 1
Complement Law
A.B = B.A
A + B = B + A
Commutative Law
𝐴̿ = A
Double Complement Law
A(B + C) = A.B + A.C
A + (B.C) = (A + B).(A + C)
Distributive Law
A + (A.B) = A
A(A +B) = A
Absorptive Law
A + (B + C) = (A + B) + C = A + B + C
A(B.C) = (A.B)C = A.B.C
Associative Law
