Digital Logic Symbols For Logic gates

Presentasi berjudul: "Digital Logic Symbols For Logic gates"— Transcript presentasi:

1 Digital Logic Symbols For Logic gates
Gerbang OR identik dengan saklar parallel Gerbang AND identik dengan saklar seri

2 Digital Logic Symbols For Logic gates

3 Digital Logic Universal gates

4 Digital Logic Universal gates

5 Digital Logic Multiple Input gates

6 Digital Logic Multiple Input / output gates

7

8 Digital Circuits and Relationship to Boolean Algebra

9 CONTOH. Buatlah rangkaian dengan Gerbang Logika untuk aljabar Boolean sbb. X . ( X’ + Y ) Jawab. X X.( X’+Y) Y

10 Logic Diagrams and Expressions
Truth Table 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 X Y Z Z Y X F × + = Equation Z Y X F + = X Y F Z Logic Diagram Boolean equations, truth tables and logic diagrams describe the same function! Truth tables are unique; expressions and logic diagrams are not. This gives flexibility in implementing functions.

11 Contoh : Buatlah persamaan boolean dan rangkaian logika dari fungsi boolean dalam bentuk Minterm sbb F(ABC) =  ( 0,3,6,7 )

12 = A’B’C’ + A’BC + ABC’ + ABC = A’(B’C’ + BC) + AB(C’ + C)
Persamaan Boolean F =  Fi = F0 + F3 + F6 + F7 = A’B’C’ + A’BC + ABC’ + ABC = A’(B’C’ + BC) + AB(C’ + C) = A’(B C) + AB Rangkaian logika F(ABC) = A(B C) + AB A B C

13 Tentukan output dari rangkaian logika dibawah !
Rangkaian yang mana outputnya dalam bentuk POS, atau SOP ?

14 Tentukan output dari rangkaian logika dibawah !
Apakah outputnya dalam bentuk POS, atau SOP ?

15

16 Buffer A buffer is a gate with the function F = X:
In terms of Boolean function, a buffer is the same as a connection! So why use it? A buffer is an electronic amplifier used to improve circuit voltage levels and increase the speed of circuit operation. X F

17 XOR/XNOR (Continued) Z Y X Å Å + + + = = Y Z ) ( X 1 Å = =
The XOR function can be extended to 3 or more variables. For more than 2 variables, it is called an odd function or modulo 2 sum (Mod 2 sum), not an XOR: The complement of the odd function is the even function. The XOR identities: Z Y X Å Å + + + = X 1 Å = Y Z ) ( = =

18 IC LOGIC

19 IC LOGIC

20 Gates

21 IC LOGIC Digital IC types SSI- few gates, basic logic operations
MSI gates, performs complete logic function LSI- more than 100 gates VLSI- thousands of gates

22 Expression Simplification
An application of Boolean algebra Simplify to contain the smallest number of literals (complemented and uncomplemented variables): = AB + ABCD + A C D + A C D + A B D = AB + AB(CD) + A C (D + D) + A B D = AB + A C + A B D = B(A + AD) +AC = B (A + D) + A C 5 literals + D C B A

23 Simplify the following boolean function to a minimum number of literals.
X+x’y=(x+x’)(x+y)=x+y X(x’+y)=xx’+xy=0+xy=xy X’y’z+x’yz+xy’=x’z(y’+y)+xy’=x’z+xy’ Xy+x’z+yz=xy+x’z+yz(x+x’) =xy+x’z+xyz+x’yz =xy(1+z)+x’z(1+y) =xy+x’z 5. (x+y)(x’+z)(y+z)=(x+y)(x’+z)

24