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

Digital Logic Symbols For Logic gates

Digital Logic Universal gates

Digital Logic Universal gates

Digital Logic Multiple Input gates

Digital Logic Multiple Input / output gates

Digital Circuits and Relationship to Boolean Algebra

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

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.

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

= 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

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

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

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

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 ) ( = =

IC LOGIC

IC LOGIC

Gates

IC LOGIC Digital IC types SSI- few gates, basic logic operations MSI- 10-100 gates, performs complete logic function LSI- more than 100 gates VLSI- thousands of gates

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

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)