Digital Logic “102” 12 Jan 2016 Mark Schmalz cise.ufl/~mssz/CompOrg/Top-Level.html

1. CDA 3101 Spring 2016Introduction to Computer Organization Digital Logic “102” 12 Jan 2016 Mark Schmalz http://www.cise.ufl.edu/~mssz/CompOrg/Top-Level.html

2. Overview • Review of gates and truth tables • Boolean algebra • Complex logic circuits • Combinational logic systems • Clocking • Memory elements

3. Transistors Symbol Functional Behavior NOT gate (Inverter)

4. Gate Symbol Truth Table NOT Gate NAND Gate

5. AND, OR, NOR Gates NOR

6. Boolean Algebra • Basic operators: OR (sum), AND (product), NOT • Boolean laws:

7. Circuit Equivalence

8. M = ABC + ABC + ABC + ABC The Majority Function M = f (A, B, C)

9. M = ABC + ABC + ABC + ABC The Majority Function (cont’d) M = f (A, B, C) Step 1. Build truth table for logic function f. Step 2. Write logic equation in SOP form. 3b 1 1 0 3a Step 3.a) Build SOP circuit using minterms (M=1); b) OR minterms

10. Combinatorial Logic • Many inputs and many outputs • Outputs are uniquely determined by inputs • Absence of memory elements • Basic combinatorial circuits • Multiplexers • Demultiplexers • Decoders • Comparators

11. Multiplexer 2n data inputs 1 data output n control inputs

12. Decoder n data inputs 2n data outputs 3-to-8 decoder

13. Comparator

14. Two-Level Logic PLA 12 inputs 6 outputs x

15. Clocks Clock period

16. Edge-Triggered Clocking State Element 1 State Element 2 Combinational logic State Element Combinational logic

17. NOR SR Latch State 0 State 1 S - set Inputs Outputs: Q and Q R - reset

18. Clocked SR Latch

19. Clocked D Latch D C Q

20. D flip-flop D D Q D Q Q D latch D latch Q C C Q C Setup time D hold time C Q

21.  Conclusions • Digital logic – lowest level of CDA3101 worldview • Digital logic circuits • Made from building blocks (AND,OR,NOT,…) • Simple or Complex, Combinatorial • Synchronous (clocked) or Asynchronous • Know rules for Boolean Algebra Enjoy your week!!