1. Logic Gates and Boolean Algebra Introduction to Logic II

2. Objectives Know (or refresh your knowledge) on logic gates. Be able to express a logic gate in Boolean algebra. Be able to simplify some Boolean expressions.

3. Truth Tables (a reminder) Complete the truth tables for:  AND  OR  NOT etc.. What are the other names for NOT (P AND Q), NOT (P OR Q)? What is P XOR Q?

4. Circuits in Machines Processors use logic gates to perform logical operations. We are interested in using the least number of gates possible – why?

5. Boolean Logic The propositions (eg P, Q, R) are thought of as the electrical inputs – either 0 or 1. The output (eg X) is the result – this is only one bit. P OR QP + Q P AND QP. Q NOT PP

6. More Complex Expressions Given three inputs A, B, C, the output X is 1 if A is 0 and B is 1, or B is 0 and C is 1. Given three inputs A, B, C, the output X is 0 if A and B are both 1, C is 0, or A and C are both 1. Now do part ‘a’ of the two questions.

7. Logic Gates We need logic gates for AND, OR, NOT. Copy down the gates. The previous expressions can be written as linked gates. Now do part ‘b’ of the two questions.

8. More Logic Gates There are logic gates for NAND, NOR and XOR. Copy these down. There are no algebraic symbols for these gates so how do we express them in Boolean algebra?

9. Question 1 Express Q using the variables w, x, y, z for the following circuit: Q

10. Question 2 and 3 Construct a logic circuit using only NAND gates for the Boolean expression:  (A.B). (B.A) Construct a logic circuit using only NOR gates for the Boolean expression:  (A + B) + (A + B)