The Boolean expression for an OR gate is represented as ( A + B ), where ( A ) and ( B ) are the input variables. In this expression, the output is true (1) if at least one of the inputs ( A ) or ( B ) is true. If both inputs are false (0), the output will also be false.
One use of Boolean algebra is to minimize any function or logic gate.
The idea is to get a simpler expression. If you need to build the hardware to implement a specific boolean expression, you can actually save money if the expression is simpler - and thus, you need less components.
The combination of gates that does not allow the implementation of an arbitrary Boolean function is the AND gate combined with the NOT gate (NAND gate). This setup can only create functions that are monotonic, meaning they cannot represent functions that require both positive and negative inputs. To implement any arbitrary Boolean function, at least one of the following gates is needed: OR, XOR, or NOR.
a+C+BD+B
(a'b+b'a)'
Out= A'B'C+AB'C'+AC'A'+ABC
For 2-input EX-OR gate, if one input is A, the other input is B, and the output is Y. Then the Boolean expression for EX-OR (XOR) function (gate) is Y=A⊕B The output Y is true if either input A or if input B is true, but not both.Y= ( (A and NOT B) or (NOT A and B) ) ;
In a boolean algebraic expression if the ^ is replaced by v and v replaced by ^ then that becomes dual of that boolean expression.
There are two forms of the NAND gate. Inverted input: Ouput = not Input1 and not Input2 and not Input3 ... Inverted output: Output = not (Input1 and Input2 and Input3 ...)
The gate is called EXNOR gate. its output is high when only one input is high. the Boolean expression for this gate for two inputs A and B is AB+A'B'
An AND gate is a logic gate performing a Boolean logic AND operation.
Construct circuit for Boolean expression (Mention out put at each step) (PÚ~ Q) Ù (P Ú Q)
need help to simplify boolean expression
demorganization is used to reduce the Boolean expressions
Boolean expression
One use of Boolean algebra is to minimize any function or logic gate.