Boolean logic

Papabravo

Joined Feb 24, 2006
12,767
As written it is ambiguous. Does -BC mean "not B and C" or does it mean "not (B and C). You can either use parentheses or transform the expression to reverse Polish notation.
 

Dave

Joined Nov 17, 2003
6,970
As written it is ambiguous. Does -BC mean "not B and C" or does it mean "not (B and C). You can either use parentheses or transform the expression to reverse Polish notation.
If I'm not mistaken, rewriting the expression with parentheses as AB + (-A-(BC)), it is also in minimal form (consider the expression using DeMorgans theorum).

With only one of exach term I don't see how this can be simplified.

Dave
 
AB+(-A-BC). -A & -B means not A and Not B

IF expression
(1)
AB+A'+(BC)' (use "(XY)'=X'+Y' " )
=AB+A'+B'+C'; (use "X+X'Y=X+Y" )
=A'+(B+B')+C'; (USE"X+X'=1")
=A'+1+C' (USE"1+X=1")
=1

IF expression
(2)AB+A'+B'C
=AB+A'+B'C; (use "X+X'Y=X+Y" )
=A'+B+B'C'; (use "X+X'Y=X+Y" )
=A'+B+C' ;
 

Papabravo

Joined Feb 24, 2006
12,767
AB+(-A-BC). -A & -B means not A and Not B

IF expression
(1)
AB+A'+(BC)' (use "(XY)'=X'+Y' " )
=AB+A'+B'+C'; (use "X+X'Y=X+Y" )
=A'+(B+B')+C'; (USE"X+X'=1")
=A'+1+C' (USE"1+X=1")
=1

IF expression
(2)AB+A'+B'C
=AB+A'+B'C; (use "X+X'Y=X+Y" )
=A'+B+B'C'; (use "X+X'Y=X+Y" )
=A'+B+C' ;
I think you copied the original expression incorrectly. There are only two terms, not three.
 
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