A truth table for (A AND B) OR NOT C

In this video, we complete a truth table using AND, OR, and NOT.

Question one. Fill in the truth table for (A AND B) OR NOT C.

First, evaluate A AND B and NOT C separately, then apply OR. AND gives one only when both inputs are one; NOT flips its input. OR gives one when at least one input is one.

For inputs zero, zero, zero, A AND B is zero and NOT C is one, so the result is one. For inputs zero, zero, one, A AND B is zero and NOT C is zero, so the result is zero. For inputs zero, one, zero, A AND B is zero and NOT C is one, so the result is one.

For inputs zero, one, one, A AND B is zero and NOT C is zero, so the result is zero. For inputs one, zero, zero, A AND B is zero and NOT C is one, so the result is one. For inputs one, zero, one, A AND B is zero and NOT C is zero, so the result is zero.

For inputs one, one, zero, A AND B is one and NOT C is one, so the result is one. For inputs one, one, one, A AND B is one and NOT C is zero, so the result is one. Notice that when A and B are both one, the result stays one regardless of C.

Hence, the final column is one, zero, one, zero, one, zero, one, one, in binary input order.