1. B OOLEAN A LGEBRA AND LOGIC GATES Chapter2-Lecture5

2. A GENDA SOP and POS Digital logic gates Digital logic families

3. SOP AND POS Determine if the following are POS or SOP: (A+B’+C)(A+B’)(B+C’) POS A’BC + AB’C + BC SOP

4. E XERCISE 1 : Write a Boolean SOP expression for this truth table, then simplify that expression as much as possible, and draw a logic gate circuit equivalent to that simplified expression: ABCF 0000 0010 0101 0110 1000 1010 1101 1110

5. S OLUTION : Original SOP: F = A’BC’ + ABC’ = BC’(A’+A) since A + A’ = 1 = BC’ B C F

6. E XERCISE 2: WRITE SOP AND POS ABCF 0001 0010 0101 0110 1000 1011 1101 1110 SOP : F = A’B’C’ + A’BC’ + AB’C + ABC’ = A’C’(B’+B) + A(B’C + BC’) = A’C’ +A(B C) POS : (F’)’ = (A’B’C+A’BC+AB’C’+ABC)’ = (A’B’C)’(A’BC)’(AB’C’)’(ABC)’ = (A+B+C’)(A+B’+C’)(A’+B+C)(A’+B’+C’) Next slide

7. D IGITAL LOGIC GATES inverter

8. M ORE GATES Buffer F = X XF XF

9. M ORE GATES F = AB’ + A’B = A B

10. M ORE GATES F = AB + A’B’ = (A B)’

11. N OTES : All the gates except the inverter and buffer can be extended to have more than 2 inputs. The multi-input gate have the same properties of the 2 input gate. Example: x + y = y + x commutative (x + y) + z = x + (y + z) = x + y + z associative NOR NAND operators are not associative NOR : i.e.( x y) z = x ( y z ) ( x y) z = [(x + y)’ +z ]’ = (x + y)z’ = xz’ + yz’ x ( y z ) =[ x + (y + z)’]’ = x’(y + z)= x’y + x’z

12. D EFINITIONS : NOR : x y z = (x + y + z)’ NAND : x y z = (xyz)’

13. D IGITAL LOGIC FAMILIES : Digital integrated circuits can be classified by: 1. Complexity 2. Logical operation 3. Circuit technology ( digital logic family )  Basic circuit in each technology NAN,NOR, or inverter gate.  The most popular families:  TTL: transistor-transistor logic  ECL: emitter-coupled logic  MOS: metal-oxide semiconductor  CMOS: complementary metal-oxide semiconductor

14. M AIN FEATURE OF EACH : TTL: the standard logic family for a long time ECL: useful for systems that require high speed operation. MOS: suitable for circuits that need high component density CMOS: for systems requiring low-power consumption such as digital camera.