Simplify 0 ⊕ 1 - eMathHelp

The calculator will simplify the boolean expression

0 \oplus 1

, with steps shown.

Expression:

Calculate the forms?

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Simplify the boolean expression $0 \oplus 1$ .

Apply the formula $x \oplus y = \left(x \cdot \overline{y}\right) + \left(\overline{x} \cdot y\right)$ with $x = 0$ and $y = 1$ :

{\color{red}\left(0 \oplus 1\right)} = {\color{red}\left(\left(0 \cdot \overline{1}\right) + \left(\overline{0} \cdot 1\right)\right)}

Apply the negation law $\overline{1} = 0$ :

\left(0 \cdot {\color{red}\left(\overline{1}\right)}\right) + \left(\overline{0} \cdot 1\right) = \left(0 \cdot {\color{red}\left(0\right)}\right) + \left(\overline{0} \cdot 1\right)

Apply the negation law $\overline{0} = 1$ :

\left(0 \cdot 0\right) + \left({\color{red}\left(\overline{0}\right)} \cdot 1\right) = \left(0 \cdot 0\right) + \left({\color{red}\left(1\right)} \cdot 1\right)

Apply the dominant (null, annulment) law $x \cdot 0 = 0$ with $x = 0$ :

{\color{red}\left(0 \cdot 0\right)} + \left(1 \cdot 1\right) = {\color{red}\left(0\right)} + \left(1 \cdot 1\right)

Apply the commutative law:

{\color{red}\left(0 + \left(1 \cdot 1\right)\right)} = {\color{red}\left(\left(1 \cdot 1\right) + 0\right)}

Apply the identity law $x + 0 = x$ with $x = 1 \cdot 1$ :

{\color{red}\left(\left(1 \cdot 1\right) + 0\right)} = {\color{red}\left(1 \cdot 1\right)}

Apply the identity law $x \cdot 1 = x$ with $x = 1$ :

{\color{red}\left(1 \cdot 1\right)} = {\color{red}\left(1\right)}

$0 \oplus 1 = 1$

Simplify 0⊕10 \oplus 10⊕1