Combinational Logic Analysis

1. Combinational Logic Analysis

2. AB A B X=AB+CD C D CD Basic Combinational Logic Circuits • AND-OR logic • AND-OR logic produces an SOP expression. • In general, an AND-OR circuit can have any number of AND gates each with any number of inputs. SOP

3. AB A B X=AB+CD C D CD Basic Combinational Logic Circuits

4. AB A B X=AB+CD C AB+CD POS D CD Basic Combinational Logic Circuits • AND-OR-Invert logic

5. A B Basic Combinational Logic Circuits • Exclusive-OR logic XOR

6. A XOR B X A X B Basic Combinational Logic Circuits • Exclusive-NOR logic

7. Implementing Combinational Logic • Boolean expression  logic circuit • For every Boolean expression there is a logic circuit, and for every logic circuit there is a Boolean expression What’s the benefit? >> Less overall propagation delay <<

8. Implementing Combinational Logic

9. Implementing Combinational Logic • Truth table  logic circuit • If you begin with a truth table of an expression, you can write the SOP expression from the truth table and then implement the logic circuit. • Remember? SOP  AND-OR implementation.

10. Truth table  logic circuit

11. Truth table  logic circuit

12. Minimizing Logic & Implementation

13. Minimizing Logic & Implementation

14. Universal Gates • The NAND gate

15. Universal Gates • The NOR gate

16. Logic Circuit Operation with Pulse • How can we deal with combinational logic circuits with pulse waveform inputs? • The operation of each gate is the same for pulse waveform inputs as for constant-level inputs. • The output of a logic circuit at any given time depends on the inputs at that particular time, so the relationship of the time-varying inputs is of primary importance.

17. Logic Circuit Operation with Pulse • Let’s get to the basic with a given individual gate:

18. Logic Circuit Operation with Pulse

19. Logic Circuit Operation with Pulse