3. Combining gates (2)

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

Task: Write down the boolean expression for this.

Step 1: The output of the AND gate is $$ z = A.B$$ which is feeding into the NAND gate.

Step 2: The output of the OR gate is $$ y = C + D$$

Step 3: These are the inputs to the NAND gate, so write each term then add a dot between terms and an overall bar

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

which is the answer.