# Boolean logic

#### dagarve

Joined Nov 4, 2006
1
need help:

how do I simplify this equation. AB+(-A-BC). -A & -B means not A and Not B.

#### Papabravo

Joined Feb 24, 2006
15,127
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.

#### Papabravo

Joined Feb 24, 2006
15,127
need help:

how do I simplify this equation. AB+(-A-BC). -A & -B means not A and Not B.

Rewriting the expression with parentheses as AB + (-A-B)C
This expression is already in minimal form. There are no common factors, and thus there is no simplification. Why do you think that there is?

#### 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

#### vikram_kumar

Joined Nov 2, 2006
3
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
15,127
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.