NAMA :
Rio Musa Darmawan
Kelas :
2A Teknik Informatika
Matkul : Sistem Digital dan
Gelombang
Gerbang Logika
dan Aljabar Boolean.
·
Aljabar Boolean adalah alat yang
penting dalam menggambarkan, menganalisa, merancang, dan mengimplementasikan
rangkaian digital
Konstanta
Boolean dan Variabel.
·
Aljabar Boolean dibawah ini hanya mempunyai
dua nilai : 0 dan 1.
·
Logika 0 dapat dikatakan : false, off,
low, no, saklar terbuka.
·
Logika 1 dapat dikatakan : true, on, high,
yes, saklar tertutup.
·
Tiga operasi logika dasar : OR, AND,
dan NOT.
Tabel
Kebenaran.
·
Sebuah tabel kebenaran menggambarkan
hubungan antara input dan output sebuah rangkaian logika.
·
Jumlah the number of entries
corresponds to the number of inputs. For example a 2 input table would have 22
= 4 entries. A 3 input table would have
23 = 8 entries.
Operasi OR
dengan gerbang OR
·
The Boolean expression for the OR
operation is X = A+B
o
This is read as “X equals A or B.”
o
X = 1 when A = 1 or B = 1.
·
Truth table and circuit sysmbol for a
two input OR gate:
OR Operation With OR Gates
·
The OR operation is similar to
addition but when A = 1 and B = 1, the OR operation produces 1+1=1.
·
In the Boolean expression
X=1+1+1=1
We could say in English that x is
true (1) when A is true (1) OR B is true (1) OR C is true (1).
·
The are many example of applications
where an output function is desired when one of multiple inputs is activated.
AND Operations with AND gates
·
The Boolean expression for the AND
operation is X = A • B
·
This is read as “X equals A and B”
·
X = 1 when A = 1 and B = 1.
·
Truth table and circuit symbol for a
two input AND gate are shown. Notice the difference between OR and AND gates.
Operation
With AND Gates
·
The AND operation is similar to
multiplication.
·
In the Boolean expression
X = A • B • C
X = 1 only when A = 1, B = 1, and C = 1.
NOT Operation
·
The Boolean expression for the NOT
operation is
X = A
·
This is read as :
o
X equals NOT A, or
o
X equals the inverse of A, or
o
X equals the complement of A
Describing Logic
Circuits Algebraically.
·
The three basic Boolean operations (OR,
AND, NOT) can describe any logic circuit.
·
If an expression contains both AND
and OR gates the AND operation will be performed first, unless there is a
parenthesis in the expression.
·
The output of an inverter is
equivalent to the input with a bar over it. Input A through an inverter equals
A.
·
Examples using inverters.
Evaluating Logic
Circuit Outputs
·
Rules for evaluating a Boolean
expression:
o
Perform all inversions of single
terms.
o
Perfotm all operations within parenthesis.
o
Perform AND operation before an OR
operation unless parenthesis indicate otherwise.
o
If an expression has a bar over it,
perform the operations inside the expression and then invert the result.
o
Output logic levels can be determined
directly from a circuit diagram
o
The output of each gate is noted
until a final output is found
Implementing
Circuits From Boolean Expressions
·
It is important to be able to draw a logic
circuit from a Boolean expression.
·
The expression x = A⋅B⋅C
Could be drawn as a three input AND gate.
·
A more complex example such as y
= AC + B C + ABC
· Could be drawn as two 2- input AND gates and one 3- input AND gate feeding into a 3.
