1. Gates and Circuits

2. Three Main Gates  AND  OR  NOT

3. NAND Gates  NOT AND TFF TTF TFT FTT A NAND BBA

4. Gate Diagrams  Example: MR + S

5. Gate Diagrams  Example:

6. Gate Diagrams  Example: (MR + S) (RS)’

7. Gate Diagrams  Exercise:

8. Truth Table (to Expression) to Gates  First, build the Boolean algebra expression that gives Z Z = AB + A’B’ TFF FTF FFT TTT ZBA

9. Truth Table to Gates  Z = AB + A’B’  Next, build the circuit that goes with the Boolean algebra expression Z TFF FTF FFT TTT ZBA

10. Z = AB + A’B’

11. Boolean Expression to Gates  Exercise: (A + B’) A

12. Boolean Expression to Gates  Exercise: (A + B’) A

13. Multi-input AND and OR  What circuit corresponds to ABC?  A+B+C?

14. Binary Addition  The first step in building our computer…

15. Binary Addition TrueFalse True False 10110 + 1+ 0+ 1+ 0 1100 Sum Carry

16. Binary Addition 000 010 001 111 CarryBA 000 110 101 011 SumBA

17. Sum Circuit 000 110 101 011 SumBA Sum = AB’ + A’B

18. Carry Circuit 000 010 001 111 CarryBA Carry = AB

19. Half Adder - Sum and Carry

20. Full Adder

21. 4 Bit Adder  Computers represent numbers in parallel.

22. Exercises  Give Boolean expressions and construct circuits with the following properties (using AND, OR or NOT gates):

23. Exercises A)B)‏ 100 110 101 011 ZBA 0000 1100 1010 0110 1001 0101 0011 1111 ZCBA

24. Exercises  2 - Fill in a truth table and give a Boolean expression for the following circuit.