1. Logic Gates

2. Outline  Logic Gates  The Inverter  The AND Gate  The OR Gate  The NAND Gate  The NOR Gate  The XOR Gate  The XNOR Gate  Drawing Logic Circuit  Analysing Logic Circuit

3. Outline  Logic Gates  The Inverter  The AND Gate  The OR Gate  The NAND Gate  The NOR Gate  The XOR Gate  The XNOR Gate  Drawing Logic Circuit  Analysing Logic Circuit

4. Logic Gates  Gate Symbols EXCLUSIVE OR abab a.b abab a+b aa' abab (a+b)' abab (a.b)' abab a  b abab a.b & abab a+b 11 AND aa' 1 abab (a.b)' & abab (a+b)' 11 abab a  b =1 OR NOT NAND NOR Symbol set 1 Symbol set 2 (ANSI/IEEE Standard 91-1984)

5. Logic Gates: The Inverter  The Inverter AA' A  Application of the inverter: Complement. 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 Binary number 1’s Complement

6. Logic Gates: The AND Gate (1/2)  The AND Gate ABAB A.B & ABAB

7. Logic Gates: The AND Gate (2/2)  Application of the AND Gate 1 sec A Enable A Counter Reset to zero between Enable pulses Register, decode and frequency display

8. Logic Gates: The OR Gate  The OR Gate 11 ABAB A+B ABAB

9. Logic Gates: The NAND Gate  The NAND Gate & ABAB (A.B)' ABAB ABAB  NAND Negative-OR 

10. Logic Gates: The NOR Gate  The NOR Gate NOR Negative-AND  11 ABAB (A+B)'  ABAB ABAB

11. Logic Gates: The XOR Gate  The XOR Gate =1 ABAB A  B ABAB

12. Logic Gates: The XNOR Gate  The XNOR Gate ABAB (A  B)' =1 ABAB (A  B)'

13. Outline  Logic Gates  The Inverter  The AND Gate  The OR Gate  The NAND Gate  The NOR Gate  The XOR Gate  The XNOR Gate  Drawing Logic Circuit  Analysing Logic Circuit

14. Drawing Logic Circuit (1/2)  When a Boolean expression is provided, we can easily draw the logic circuit.  Examples: (i) F1 = x.y.z' (note the use of a 3-input AND gate) x y z F1 z'

15. Drawing Logic Circuit (2/2) (ii) F2 = x + y'.z (if we assume that variables and their complements are available) (iii) F3 = x.y' + x'.z x y' z F2 y'.z x' z F3 x'.z x.y' x y'

16. Outline  Logic Gates  The Inverter  The AND Gate  The OR Gate  The NAND Gate  The NOR Gate  The XOR Gate  The XNOR Gate  Drawing Logic Circuit  Analysing Logic Circuit

17. Analysing Logic Circuit  When a logic circuit is provided, we can analyse the circuit to obtain the logic expression.  Example: What is the Boolean expression of F4? A'.B' A'.B'+C(A'.B'+C)' A' B' C F4 F4 = (A'.B'+C)' = (A+B).C'