2. Combining gates (1)

Let us consider combining three logic gates to end up with a single output Q. This is the drawing:

This has an AND gate feeding an OR gate that then goes through a NOT gate for output Q. It has three inputs A,B,C. Intermediate values are labelled z,y.

Task: Write down the boolean expression for this.

Step 1: The output of the AND gate is $$ z = A.B$$ which becomes an input to the OR gate

Step 2: The input to the OR gate is $z$ (from above) and input $C$. Apply an OR operation to both of these inputs, thus

$$ y = (A.B) + C$$

Step 3: Value y is fed through the NOT gate and so negation needs to be applied to get the final output Q :

$$Q= \overline{(A.B) + C}$$

which is the answer.