Boolean Identities

• If you need to check whether two expressions are equivalent, you'll need to build 2 tables, one for each expression. You may, if wanted, 'glue' these tables to one another to create a single, longer table.
• Two expressions are equivalent if and only if the sequences of bits underneath the columns for each of these expressions are identical. In the example for $(x+y)'$ and $x'y'$, we saw that the sequence of bits for each of these was $1, 0, 0, 0$.
• If the sequences of bits differ from one another, even in just one of the bits, the two expressions are not equivalent.

---

Let's verify a couple more identities. The truth table for the identity $1x = x$ is:

$1$	$\boldsymbol x$	$\boldsymbol{1\cdot x}$
$1$	$0$	$0$
$1$	$1$	$1$

Since the bits under $x$ and under $1\cdot x$ are the same (i.e., $[0, 1]$), we successfully confirmed the identity.