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Example #1
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The Task

For your next project do you need a digital circuit with
three inputs A, B, C and one output F.
F = f(A,B,C)

If the input C=1 must the output F = A&B, else if C=0 then must F=A#B

  Please note the notation:  & = AND,  # = OR,   $ = XOR,  ! = NOT
Alternative notations used:  * = AND,  + = OR, :+: = XOR  / = NOT
 

Truth table

 

Function table  

Min-Term list  
Boolean equation

 
AND-OR logic
S.O.P.
Max-Term list    F = Π(A,B,C)  (0,1,3,5)
Boolean equation  
 
OR-AND logic
P.O.S.
Ad hoc solution