Expression Form Types

This means that the expression $E$ is true when $x'yz'$, or when $x'yz$, or when $xyz$.

We can combine these 3 instances using the OR (+) symbol: $E = x'yz' + x'yz + xyz$.

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Note that the sum-of-products form isn't the simplest (= shortest) form of an expression: we can further simplify $x'yz' + x'yz + xyz$ using the identities to get a simpler sum-of-products form: $x'y + yz$.

On homework and exams, when asked to find the sum-of-products form from a truth table, you don't need to simplify the expression you got. If you are asked to simplify it further, you should use the tool at https://www.boolean-algebra.com/.

Another way to simplify Boolean expressions is by using handy tables called Karnaugh maps, which will be the last topic of these lecture notes.