How do I simplify Boolean simplification ABC + AB' . ( A' C') + A'BC?

[adnankhuram]

ABC + AB' . ( A' C') + A'BC

I am confused in AB' . ( A' C')

the multiplication would be AA'B'C' OR AA'C'+A'B'C'

 

[ehild]

ABC + AB' . ( A' C') + A'BC

I am confused in AB' . ( A' C')

the multiplication would be AA'B'C' OR AA'C'+A'B'C'

It is AA'B'C'.

ehild

 

[adnankhuram]

Abc + ab' . ( a' c') + a'bc

abc + aa'b'c' + a'bc

abc + b'c' + a'bc ( aa' = 0)

bc(a + b'c' +a')

bc (a+a'+b'c') as a+a' = 1

bc( b'c')

bb'cc'

0

is this is right

 

[ehild]

Abc + ab' . ( a' c') + a'bc

abc + aa'b'c' + a'bc

abc + b'c' + a'bc ( aa' = 0)

As aa'=0 the second term cancels. You have abc+a'bc. Continue from here.

ehild

 

[asteriatic]

Boolean simplification is a process used to simplify logical expressions in Boolean algebra. In this case, the expression ABC + AB' . ( A' C') + A'BC can be simplified by using the distributive property and the identity law of Boolean algebra.

First, we can distribute AB' across the parentheses to get AB'AC' + A'BC. Then, we can use the identity law to simplify AB'AC' to AB'C' and A'BC to A'BC.

This simplifies the expression to AB'C' + A'BC, which can also be written as A(B'C' + BC). This is the simplest form of the expression and cannot be further simplified using Boolean rules.

In summary, the simplified expression is A(B'C' + BC).